Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Advertisements
рдЙрддреНрддрд░
Let the two zeroes of the f(t) = kt2 + 2t + 3k ЁЭСПЁЭСТ α and β
Sum of the zeroes (α + β)
Product of the zeroes αβ
`-2/k=(3k)/k`
`−2k = 3k^2`
`2k + 3k^2 = 0`
`k(3k + 2) = 0`
`k = 0`
`k=(-2)/3`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If a and are the zeros of the quadratic polynomial f(x) = ЁЭСе2 − ЁЭСе − 4, find the value of `1/alpha+1/beta-alphabeta`
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
Find the zeroes of the quadratic polynomial `2x^2 ╦Ч 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `(3x^2 ╦Ч x ╦Ч 4)` and verify the relation between the zeroes and the coefficients.
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, -2 and -24 respectively.
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
If ЁЭЫ╝, ЁЭЫ╜ are the zeroes of the polynomial f(x) = x2 + x – 2, then `(∝/β-∝/β)`
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
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.
`(-8)/3, 4/3`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`7y^2 - 11/3 y - 2/3`
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
