Advertisements
Advertisements
प्रश्न
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
विकल्प
-1
1
-9
9
Advertisements
उत्तर
Let `alpha = 3` and `beta = -3` be the given zeros and y be the third zero of the polynomial `x^3 + x^2 -9x-9` then
Bt using `alpha + beta + y = (-text{coefficient of }x^2)/(text{coefficient of } x^3)`
`alpha + beta + y = -1/1`
`alpha + beta + y = -1`
Substituting `alpha = 3` and `beta =-3` in `alpha + beta + y = -1`, we get
` 3 - 3 + y =-1`
`y = -1`
Hence, the correct choice is `(a).`
APPEARS IN
संबंधित प्रश्न
if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
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 α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
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.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero 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:
`2x^2 + (7/2)x + 3/4`
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`7y^2 - 11/3 y - 2/3`
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
