Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
Let p(x) = `4x^2 + 5sqrt(2)x - 3`
= `4x^2 + 6sqrt(2)x - sqrt(2)x - 3`
= `2sqrt(2)x (sqrt(2)x + 3) - 1(sqrt(2)x + 3)`
= `(sqrt(2)x + 3)(2sqrt(2)x – 1)`
So, the zeroes of p(x) = `- 3/sqrt(2)` and `1/(2sqrt(2))`
∴ Sum of zeroes = `- 3/sqrt(2) + 1/(2sqrt(2))`
= `- 5/(2sqrt(2))`
= `(-5sqrt(2))/4`
= `(-("coefficient of" x))/("coefficient of" x^2)`
And product of zeroes = `- 3/sqrt(2) . 1/(2sqrt(2)) = - 3/4`
= `"constant term"/("coefficient of" x^2)`
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 quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
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(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
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.
If one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 − 3abc + a2d = 0.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
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.
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, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
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 the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.
