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:
5t2 + 12t + 7
Advertisements
उत्तर
5t2 + 12t + 7
Splitting the middle term, we get,
5t2 + 5t + 7t + 7
Taking the common factors out, we get,
5t(t + 1) + 7(t + 1)
On grouping, we get,
(t + 1)(5t + 7)
So, the zeroes are,
t + 1 = 0
`\implies` y = –1
5t + 7 = 0
`\implies` 5t = –7
`\implies` t = `-7/5`
Therefore, zeroes are `(-7/5)` and –1
Verification:
Sum of the zeroes = – (coefficient of x) ÷ coefficient of x2
α + β = `- b/a`
`(-1) + (-7/5) = - (12)/5`
= `-12/5 = -12/5`
Product of the zeroes = constant term ÷ coefficient of x2
αβ = `c/a`
`(-1)(-7/5) = 7/5`
`7/5 = 7/5`
APPEARS IN
संबंधित प्रश्न
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
4s2 – 4s + 1
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
1, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
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 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − px + q, prove that `alpha^2/beta^2+beta^2/alpha^2=p^4/q^2-(4p^2)/q+2`
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 α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` 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.
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).
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
4x2 – 3x – 1
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
