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:
`2x^2 + (7/2)x + 3/4`
Advertisements
Solution
`2x^2 + (7/2)x + 3/4`
The equation can also be written as,
8x2 + 14x + 3
Splitting the middle term, we get,
8x2 + 12x + 2x + 3
Taking the common factors out, we get,
4x(2x + 3) + 1(2x + 3)
On grouping, we get,
(4x + 1)(2x + 3)
So, the zeroes are,
4x + 1 = 0
`\implies` x = `-1/4`
2x + 3 = 0
`\implies` x = `-3/2`
Therefore, zeroes are `-1/4` and `-3/2`
Verification:
Sum of the zeroes = – (coefficient of x) ÷ coefficient of x2
α + β = `- b/a`
`(-3/2) + (-1/4) = - (7)/4`
= `-7/4`
Product of the zeroes = constant term ÷ coefficient of x2
αβ = `c/a`
`(-3/2)(-1/4) = (3/4)/2`
= `3/8`
APPEARS IN
RELATED QUESTIONS
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
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 α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
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 f(x) = 4x2 - 4x - 3 and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
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 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
The product of the zeros of x3 + 4x2 + x − 6 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
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
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`
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`
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
