Advertisements
Advertisements
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)`
Advertisements
उत्तर १
`g(x)=a[(x^2+1)-x(a^2+1)]^2=ax^2+a-a^2x-x`
`=ax^2-[(a^2+1)-x]+0=ax^2-a^2x-x+a`
`=ax(x-a)-1(x-a)=(x-a)(ax-1)`
Zeroes of the polynomials `=1/a` and a
Sum of zeroes `=(-(a^2-1))/a`
`rArr1/a+a=(a^2+1)/a`
`rArr(a^2+1)/a=(a^2+1)/a`
Product of zeroes `=a/a`
`rArr1/axxa=a/a`
`rArr1=1`
Hence relationship verified
उत्तर २
`g(x)=a[(x^2+1)-x(a^2+1)]^2=ax^2+a-a^2x-x`
`=ax^2-[(a^2+1)-x]+0=ax^2-a^2x-x+a`
`=ax(x-a)-1(x-a)=(x-a)(ax-1)`
Zeroes of the polynomials `=1/a` and a
Sum of zeroes `=(-(a^2-1))/a`
`rArr1/a+a=(a^2+1)/a`
`rArr(a^2+1)/a=(a^2+1)/a`
Product of zeroes `=a/a`
`rArr1/axxa=a/a`
`rArr1=1`
Hence relationship verified
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
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 f(x) = ax2 + bx + c, then evaluate :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
If a and are the zeros of the quadratic polynomial f(x) = 𝑥2 − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
The number of polynomials having zeroes as –2 and 5 is ______.
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
