Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
उत्तर
By factorization method:
x2 - 2x - 8
⇒ x2 - 4x + 2x - 8 = 0
⇒ x(x - 4) + 2(x - 4) = 0
⇒ x(x - 4) + 2(x - 4) = 0
⇒ (x - 4) (x + 2) = 0
⇒ x - 4 = 0, x + 2 = 0
⇒ x = 4, x = -2
For p(x) = 0, we must have (x - 4) (x + 2) = 0 Either x - 4 = 0
x = 4
or x + 2 = 0
x = -2
∴ The zeroes of x2 - 2x - 8 are 4 and -2
Now,
= Sum of the zeroes `="-Coefficient of x"/"Coefficient of x"`
`-2+4=(-(-2))/1`
2 = 2 (L.H.S = R.H.S)
Product of the zeroes `="Constant term"/("Coefficient of "x^2)`
`-2xx4=(-8)/1`
`-8 = -8` (L.H.S = R.H.S)
Thus, the relationship between the zeroes and the coefficients in the polynomial x2 – 2x – 8 is verified.
संबंधित प्रश्न
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:
4s2 – 4s + 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 zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
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) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
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 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 two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
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?
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
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`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
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 ______.
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
