Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Advertisements
उत्तर
3x2 – x – 4
= 3x2 – 4x + 3x – 4
= x(3x – 4) + 1(3x - 4)
= (3x – 4)(x + 1)
For p(x) = 0 we have,
Either (x + 1) = 0
x = –1
or 3x – 4 = 0
`x = 4/3`
∴ The zeroes of 3x2 - x - 4 are -1 and `4/3`
Now,
Sum of the zeroes = `-("Coefficient of " x)/("Coefficient of " x^2)`
= `(-1) + 4/3`
= `(-(-1))/3`
= `1/3 = 1/3`
and product of zeroes `"Constant term"/("Coefficient of " x^2)`
`(-1)xx 4/3 = (-4)/3`
= `(-4)/3 = (-4)/3`
Thus, the relationship between the zeroes and coefficients in the polynomial 3x2 – x – 4 is verified.
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.
`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`.
If one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
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 f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x2 + x – 2, then `(∝/β-∝/β)`
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
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 quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
