Advertisements
Advertisements
प्रश्न
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
Advertisements
उत्तर
Given: α + β = `1/4`, αβ = -1
Since ax2 + bx + c = kx2 - k(α + β)x + kαβ
In comparison,
a = k, b = -k(α + β) and c = kαβ
α + β = `(-b)/a = 1/4` and αβ = `c/a = -1`
⇒ a = 4
⇒ b = -4(α + β)
⇒ c = kαβ = 4(-1)
Hence, on writing as ax2 + bx + c
⇒ 4x2 - 4(α + β)x + 4(αβ)
⇒ `4x^2 - 4(1/4)x + 4(-1)`
⇒ 4x2 - x - 4
The quadratic polynomial is 4x2 - x - 4.
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
4s2 – 4s + 1
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.
4, 1
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find 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.
Verify that 3, -2, 1 are the zeros of the cubic polynomial `p(x) = (x^3 – 2x2 – 5x + 6)` and verify the relation between it zeros and 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.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
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.
`(-3)/(2sqrt(5)), -1/2`
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.
Find a quadratic polynomial whose zeroes are 6 and – 3.
