Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
उत्तर
P(s) = 4s2 – 4s + 1
4s2 – 2s – 2s + 1 = 0
2s(2s – 1) – 1(2s – 1) = 0
(2s – 1) (2s – 1) = 0
s = `1/2`, s = `1/2`
a = 4, b = – 4, c = 1, ∝ = `1/2`, β = `1/2`
∝ + β = `(-b)/a`, ∝β = `c/a`
`1/2 + 1/2 = (-4)/4, (1/2)(1/2) = 1/4`
`(1 + 1)/2 = (+4)/4, 1/4 = 1/4`
`2/2` = 1
1 = 1
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
If a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
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 ______.
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
