Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
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 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
4s2 – 4s + 1
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
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 one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
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 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x2 + x – 2, then `(∝/β-∝/β)`
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
The zeroes of the polynomial r(t) = -12t2 + (k - 3)t + 48 are negative of each other. Then k is ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
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:
4x2 – 3x – 1
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
