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)`
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
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of `alpha^4beta^3+alpha^3beta^4`
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.
Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
