Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
Advertisements
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 polynomials and verify the relationship between the zeroes and the coefficients
`g(x)=a(x^2+1)-x(a^2+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 :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
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 zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
