Advertisements
Advertisements
Question
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
Advertisements
Solution
P(x) = 5x2 + 5x + 1
α + β = `(-b)/a = (-5)/5` = – 1
αβ = `c/a = 1/5`
α2 + β2 = (α + β)2 – 2αβ
= `(-1)^2 - 2(1/5)`
= `1 - 2/5`
= `3/5`
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-3)/(2sqrt(5)), -1/2`
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
