हिंदी

If One Zero of the Quadratic Polynomial F(X) = 4x2 − 8kx − 9 is Negative of the Other, Find the Value Of K.

Advertisements
Advertisements

प्रश्न

If one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.

Advertisements

उत्तर

Since α and -α are the zeros of the quadratic polynomial f(x) = 4x2 − 8kx − 9

α - α = 0

`(-"coefficient of x")/("coefficient of "x^2)=0`

`(-8k)/4=0`

-8k = 0 x 4

-8k = 0

`k=0/-8`

k = 0

Hence, the value of k is 0.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Polynomials - Exercise 2.1 [पृष्ठ ३४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 10
अध्याय 2 Polynomials
Exercise 2.1 | Q 14 | पृष्ठ ३४

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s2 – 4s + 1


Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

4u2 + 8u


Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 

`1/4 , -1`


If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b


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 p(s) = 3s2 − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`


If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(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 quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.


Find all the zeroes of `(x^4 + x^3 – 23x^2 – 3x + 60)`, if it is given that two of its zeroes are `sqrt3 and –sqrt3`. 


If 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?` 


Define a polynomial with real coefficients.


If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 cx + d, then α2 + β2 + γ2 =


If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is


If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then


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:

3x2 + 4x – 4


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 sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×