Advertisements
Advertisements
Question
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
Advertisements
Solution
Let p(x) = `4x^2 + 5sqrt(2)x - 3`
= `4x^2 + 6sqrt(2)x - sqrt(2)x - 3`
= `2sqrt(2)x (sqrt(2)x + 3) - 1(sqrt(2)x + 3)`
= `(sqrt(2)x + 3)(2sqrt(2)x – 1)`
So, the zeroes of p(x) = `- 3/sqrt(2)` and `1/(2sqrt(2))`
∴ Sum of zeroes = `- 3/sqrt(2) + 1/(2sqrt(2))`
= `- 5/(2sqrt(2))`
= `(-5sqrt(2))/4`
= `(-("coefficient of" x))/("coefficient of" x^2)`
And product of zeroes = `- 3/sqrt(2) . 1/(2sqrt(2)) = - 3/4`
= `"constant term"/("coefficient of" x^2)`
APPEARS IN
RELATED QUESTIONS
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.
4, 1
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case
x3 – 4x2 + 5x – 2; 2, 1, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
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 p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
Find a cubic polynomial whose zeroes are 2, -3and 4.
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2x^2 + (7/2)x + 3/4`
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`
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
