Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
Advertisements
उत्तर
h(t) `=t^2-15`
`=(t)^2-(sqrt15)^2`
`=(t+sqrt15)(t-sqrt15)`
For p(t) = 0, we have
Either `(t + sqrt15) = 0`
`t = sqrt15`
or `t - sqrt15 = 0`
`t = sqrt15`
Sum of the zeroes = `-("Coefficient of " t)/("Coefficient of " t^2)`
`-sqrt15+sqrt15=(-0)/1`
0 = 0
Also product of the zeroes = `"Constant term"/("Coefficient of "t^2)`
`-sqrt15xxsqrt15=(-15)/1`
`-15=-15`
Thus, the relationship between zeroes and the coefficients in the polynomial t2 - 15 is verified.
संबंधित प्रश्न
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 polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case
x3 – 4x2 + 5x – 2; 2, 1, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
If a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
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.
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, 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
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 `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
