Advertisements
Advertisements
Question
If α, β are the zeros of a polynomial such that α + β = −6 and αβ = −4, then write the polynomial.
Solution
Let S and P denotes respectively the sum and product of the zeros of a polynomial
We are given S = -6 and P = - 4. Then
The required polynomial g(x) is given by
`g (x) = x^2 -Sx + p`
`g (x) = x^2 - (-6)x + ( - 4)`
`= x^2 + 6x - 4`
Hence, the polynomial is `x^2 + 6x - 4`
APPEARS IN
RELATED QUESTIONS
Classify the following polynomials as polynomials in one-variable, two variables etc:
`x^2-2tx+7t^2-x+t`
The graph of the polynomial f(x) = ax2 + bx + c is as shown in Fig. 2.20. Write the value of b2 − 4ac and the number of real zeros of f(x).
If x = 1 is a zero of the polynomial f(x) = x3 − 2x2 + 4x + k, write the value of k.
If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b?
If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\] is equal to
State whether the given algebraic expression is polynomial. Justify.
`2m^(-2) + 7m - 5`
Divide. Write the quotient and the remainder.
(25m4 − 15m3 + 10m + 8) ÷ 5m3
Identify the following expression is polynomial. If not give reason:
`1/x(x + 5)`
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.
Observe the following graph and answer.
In the above graph, how many zeroes are there for the polynomial?
Determine the degree of the following polynomial:
x3 – 9x + 3x5
