Advertisements
Advertisements
प्रश्न
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`
उत्तर
Let p(x) = `4x^2 + 5sqrt(2)x - 3`
= `4x^2 + 6sqrt(2)x - sqrt(2)x - 3`
= `2sqrt(2)x (sqrt(2)x + 3) - 1(sqrt(2)x + 3)`
= `(sqrt(2)x + 3)(2sqrt(2)x – 1)`
So, the zeroes of p(x) = `- 3/sqrt(2)` and `1/(2sqrt(2))`
∴ Sum of zeroes = `- 3/sqrt(2) + 1/(2sqrt(2))`
= `- 5/(2sqrt(2))`
= `(-5sqrt(2))/4`
= `(-("coefficient of" x))/("coefficient of" x^2)`
And product of zeroes = `- 3/sqrt(2) . 1/(2sqrt(2)) = - 3/4`
= `"constant term"/("coefficient of" x^2)`
APPEARS IN
संबंधित प्रश्न
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
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 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\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
The number of polynomials having zeroes as –2 and 5 is ______.
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
