Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
Sum of the zeroes = `- 8/3`
Product of the zeroes = `4/3`
P(x) = x2 – (Sum of the zeroes) + (Product of the zeroes)
Then, P(x) = `x^2 - (-8x)/3 + 4/3`
P(x) = `3x^2 + 8x + 4`
Using splitting the middle term method,
3x2 + 8x + 4 = 0
3x2 + (6x + 2x) + 4 = 0
3x2 + 6x + 2x + 4 = 0
3x(x + 2) + 2(x + 2) = 0
(x + 2)(3x + 2) = 0
`\implies` x = `-2, -2/3`
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
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
1, 1
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
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 α2β + αβ2
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively.
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
Find the quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are 2, -3and 4.
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
