Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Advertisements
उत्तर
4u2 + 8u = 4u(u + 2)
= 4[u - 0][u - (-2)]
For p(u) = 0, we have
Either 4u = 0
u = -2
∴ The zeroes of 4u2 + 8u are 0 and -2.
Relationship between the zeroes and the coefficients of the polynomial
Sum of the zeroes = `-("Coefficient of " u)/("Coefficient of " u^2)`
= `0 + (-2) =(-(8))/4`
= -2 = -2
Also product of the zeroes = `"Constant term"/("Coefficient of " u^2)`
= `0 xx (-2) = 0/4`
= 0 = 0
Thus, the relationship between the zeroes and the coefficients in the polynomial 4u2 + 8u 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.
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
Define a polynomial with real coefficients.
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes 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 ______.
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.
`21/8, 5/16`
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`7y^2 - 11/3 y - 2/3`
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.
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
Find the zeroes of the polynomial x2 + 4x – 12.
