Advertisements
Advertisements
प्रश्न
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p.
Advertisements
उत्तर
Given α and β are the zeros of the quadratic polynomial f(x) = x2 + px + 45
`alpha+beta=-"coefficient of x"/("coefficient of "x^2)`
`=(-p)/1`
= -p
`alphabeta="constant term"/("coefficient of "x^2)`
`=45/1`
= 45
we have,
`(alpha-beta)^2=alpha^2+beta^2-2alphabeta`
`144=(alpha+beta)^2-2alphabeta-2alphabeta`
`144=(alpha+beta)^2-4alphabeta`
Substituting `alpha+beta=-p " and "alphabeta=45`
then we get,
`144=(-p)^2-4xx4`
`144=p^2-4xx45`
`144=p^2-180`
`144+180=p^2`
`324=p^2`
`sqrt(18xx18)=pxxp`
`+-18=p`
Hence, the value of p is ±18.
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
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 the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`
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 quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
Verify that 5, -2 and 13 are the zeroes of the cubic polynomial `p(x) = (3x^3 – 10x^2 – 27x + 10)` and verify the relation between its zeroes and coefficients.
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, -2 and -24 respectively.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
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`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
