Advertisements
Advertisements
Question
Find the quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.
Solution
Let 𝛼 and 𝛽 be the zeroes of the required polynomial f(x).
Then (𝛼 + 𝛽) =` 5/2 `and 𝛼𝛽 = 1
`∴ f(x)=x^2-(∝+β) x+∝β `
`⇒f(x)=x^2-5/2x+1`
`⇒ f(x)=2x^2-5x+2`
Hence, the required polynomial is `f(x)=2x^2-5x+2`
∴` f(x) = 0 ⇒ 2x^2 – 5x + 2 = 0`
⇒ `2x^2 – (4x + x) + 2 = 0`
⇒` 2x^2 – 4x – x + 2 = 0`
⇒ `2x (x – 2) – 1 (x – 2) = 0`
⇒` (2x – 1) (x – 2) = 0`
⇒ `(2x – 1) = 0 or (x – 2) = 0`
`⇒ x =1/2 or x=2`
So, the zeros of f(x) are `1/2` and 2
APPEARS IN
RELATED QUESTIONS
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
Define a polynomial with real coefficients.
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
A quadratic polynomial, whose zeroes are –3 and 4, is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
3x2 + 4x – 4
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
