Advertisements
Advertisements
प्रश्न
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
पर्याय
`(-2)/3`
`2/3`
`1/3`
`(-1)/3`
Advertisements
उत्तर
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is `underline(bb(2/3)`.
Explanation:
Given f(x) = px2 – 2x + 3p
And, α + β = αβ
Sum of zeroes = Product of zeros
`(-b)/α = c/α`
–b = c
Putting values
–(–2) = 3p
2 = 3p
3p = 2
p = `2/3`
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
Find a quadratic polynomial whose zeroes are 6 and – 3.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
