Advertisements
Advertisements
Question
If one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.
Advertisements
Solution
Since α and -α are the zeros of the quadratic polynomial f(x) = 4x2 − 8kx − 9
α - α = 0
`(-"coefficient of x")/("coefficient of "x^2)=0`
`(-8k)/4=0`
-8k = 0 x 4
-8k = 0
`k=0/-8`
k = 0
Hence, the value of k is 0.
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
`p(x) = x^2 + 2sqrt2x + 6`
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 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
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
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
What will be the expression of the polynomial?
The number of polynomials having zeroes as –2 and 5 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.
`(-3)/(2sqrt(5)), -1/2`
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
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 α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
