Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If ЁЭЫ╝, ЁЭЫ╜ are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
Advertisements
рдЙрддреНрддрд░
By using the relationship between the zeroes of he quadratic polynomial. We have
Sum of zeroes=`(-("Coefficient of x"))/("Coefficient of "x^2)`Sum of zeroes = `"Constant term"/("Coefficient of" x^2) `
∴` ∝+β=-(-7)/5 and ∝β=1/5`
⇒` ∝+β =7/5 and ∝β=1/5`
Now,`1/∝+1/β= (∝+β)/(∝β)`
=`(7/5)/(1/5)`
= 7
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
If ЁЭЫ╝ and ЁЭЫ╜ 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 `2x^2 ╦Ч 11x + 15` 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.
Find the quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
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.
`-2sqrt(3), -9`
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
