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If alpha, beta and gamma are the zeros of the polynomial ax^3 + bx^2 + cx + d, find the value of
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Polynomials class 10 important questions .
If alpha, beta and gamma are the zeroes of the polynomial p(x) = ax^3 + bx^2 + cx + d, find the value of 1/α(alpha) + 1/β(beta) + 1/γ(gamma)
#polynomialsclass10byavisir
#polynomialsclass10
#polynomialsclass10importantquestions #polynomialsclass10avijainclasses
Other important questions for class 10 polynomials are given below. Students are requested to view all the questions in the order in which I am writing them. Once you solve all of them, you can b sure of attempting almost any question that comes in your exam from this chapter.
1) If α and β are the zeroes of the polynomial x^2+5x+5, find the value of α^-1 + β^-1.
2) If α and β are the zeroes of the polynomial x^2+7x+7, find the value of 1/α + 1/β - 2αβ.
3) if α and β are the zeroes of polynomial 2x^2 - 7x + 3, then find the value of α^2 + β^2.
4) If α, β and γ are the zeroes of the polynomial p(x) = ax^3 + bx^2 + cx + d, find the value of 1/α + 1/β + 1/γ.
5) If one zero of the polynomial (a^2+9)x^2 + 13x + 6a is reciprocal of the other, find the value of a.
6) If one of the zeroes of the polynomial is equal in magnitude, but opposite in sign, then find the value of k.
7) If one zero of the polynomial 3x^2 = 8x + 2k + 1 is seven times the other, then find the zeroes and the value of k.
8) If α and β are the zeroes of f(x)= x^2-6x+k, then find the value of k if α ^2 + β ^2=40.
9) If the squared difference of the zeroes of f(x)=x^2+px+45 is 144, find p
10) If α and β are the zeroes of x^2 – 6x + k, such that α - β = 1, then find the value of k.
11) If α and β are the zeroes of x^2 – 6x + a, find the value of a, if 3α + 2β = 20
12) If α and β are the zeroes of the polynomial x^2 - 2x - 15, then find the polynomial whose zeroes are 2α and 2β.
13) Find the zeroes of y^2 + 4√3 y – 15
14) Find the zeroes of 4x^2 + 5√2 x – 3
15) If the zeroes of polynomial x^3-ax^2+bx-c are in AP, then show that 2a^3-9ab+27c=0
16) Find the zeroes of the polynomial x^3 - 13x^2 + 52x - 60 if it is given that the product of its two zeroes is 10.
17) For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5-x4-4x3+3x2+3x+b ?
18) If α, β and γ are the zeroes of polynomial kx^3 – 5x + 9 and α^3 + β^3 + γ^3 = 27, then find the value of k.
19) Is polynomial y^4 + y^2 + 5 have zeroes or not ?
20) Use factor theorem to prove that x+a is a factor of x^n + a^n if n is an odd positive integer.
21) If (x+a) is a factor of two polynomials x^2+px+q and x^2+mx+n, then prove that : a=n- q/m-p
22) If 1 and -1 are the zeroes of the polynomial Lx^4 + Mx^3 + Nx^2 + Rx + P, then show that L + N + P = M + R = 0
23)
If alpha, beta and gamma are the zeroes of the polynomial p(x) = ax^3 + bx^2 + cx + d, find the value of 1/α(alpha) + 1/β(beta) + 1/γ(gamma)
#polynomialsclass10byavisir
#polynomialsclass10
#polynomialsclass10importantquestions #polynomialsclass10avijainclasses
Other important questions for class 10 polynomials are given below. Students are requested to view all the questions in the order in which I am writing them. Once you solve all of them, you can b sure of attempting almost any question that comes in your exam from this chapter.
1) If α and β are the zeroes of the polynomial x^2+5x+5, find the value of α^-1 + β^-1.
2) If α and β are the zeroes of the polynomial x^2+7x+7, find the value of 1/α + 1/β - 2αβ.
3) if α and β are the zeroes of polynomial 2x^2 - 7x + 3, then find the value of α^2 + β^2.
4) If α, β and γ are the zeroes of the polynomial p(x) = ax^3 + bx^2 + cx + d, find the value of 1/α + 1/β + 1/γ.
5) If one zero of the polynomial (a^2+9)x^2 + 13x + 6a is reciprocal of the other, find the value of a.
6) If one of the zeroes of the polynomial is equal in magnitude, but opposite in sign, then find the value of k.
7) If one zero of the polynomial 3x^2 = 8x + 2k + 1 is seven times the other, then find the zeroes and the value of k.
8) If α and β are the zeroes of f(x)= x^2-6x+k, then find the value of k if α ^2 + β ^2=40.
9) If the squared difference of the zeroes of f(x)=x^2+px+45 is 144, find p
10) If α and β are the zeroes of x^2 – 6x + k, such that α - β = 1, then find the value of k.
11) If α and β are the zeroes of x^2 – 6x + a, find the value of a, if 3α + 2β = 20
12) If α and β are the zeroes of the polynomial x^2 - 2x - 15, then find the polynomial whose zeroes are 2α and 2β.
13) Find the zeroes of y^2 + 4√3 y – 15
14) Find the zeroes of 4x^2 + 5√2 x – 3
15) If the zeroes of polynomial x^3-ax^2+bx-c are in AP, then show that 2a^3-9ab+27c=0
16) Find the zeroes of the polynomial x^3 - 13x^2 + 52x - 60 if it is given that the product of its two zeroes is 10.
17) For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5-x4-4x3+3x2+3x+b ?
18) If α, β and γ are the zeroes of polynomial kx^3 – 5x + 9 and α^3 + β^3 + γ^3 = 27, then find the value of k.
19) Is polynomial y^4 + y^2 + 5 have zeroes or not ?
20) Use factor theorem to prove that x+a is a factor of x^n + a^n if n is an odd positive integer.
21) If (x+a) is a factor of two polynomials x^2+px+q and x^2+mx+n, then prove that : a=n- q/m-p
22) If 1 and -1 are the zeroes of the polynomial Lx^4 + Mx^3 + Nx^2 + Rx + P, then show that L + N + P = M + R = 0
23)
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