Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
Advertisements
उत्तर
6x2 – 7x – 3 = 0
⇒ 6x2 – 9x + 2x – 3 = 0
⇒ 3x(2x – 3) + 1(2x – 3) = 0
⇒ (2x – 3)(3x + 1) = 0
⇒ 2x – 3 = 0 and 3x + 1 = 0
⇒ 2x = 3 and 3x = −1
⇒ x = `3/2` and x = `(-1)/3`
Let considered x = `3/2` be α and x = `(-1)/3` be β.
α + β = `3/2 + ((-1)/3) = (9 - 2)/6 = 7/6`
`(-"b")/"a" = (-(-7))/6 = 7/6`
⇒ α + β = `(-"b")/"a"`
αβ = `3/2 xx (-1)/3 = (-1)/2`
`"c"/"a" = (-3)/6 = (-1)/2`
αβ = `"c"/"a"`
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2.
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.
If the zeros of the polynomial f(x) = x3 – 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial 2x2 – 11x + 15 and verify the relation between the zeroes and the coefficients.
The product of the zeros of x3 + 4x2 + x − 6 is
The number of polynomials having zeroes as –2 and 5 is ______.
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
