Advertisements
Advertisements
Question
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`
Solution
Let p(y) = `y^2 + 3/2 sqrt(5)y - 5`
= `2y^2 + 3sqrt(5)y - 10`
= `2y^2 + 4sqrt(5)y - sqrt(5)y - 10`
= `(y + 2sqrt(5))(2y - sqrt(5))`
So, the zeroes of p(y) are `-2sqrt(5)` and `sqrt(5)/2`
∴ Sum of zeroes = `-2sqrt(5) + sqrt(5)/2`
= `(-3sqrt(5))/2`
= `(-("coefficient of" y))/("coefficient of" y^2)`
And product of zeroes = `-2sqrt(5) xx sqrt(5)/2` = –5
= `"constant term"/("coefficient of" y^2)`
APPEARS IN
RELATED QUESTIONS
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
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 two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
Find a quadratic polynomial whose zeroes are 6 and – 3.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
