Question

Find the zeroes of the quadratic Polynomial 5x²+8x-4 and verify the relationship between zeroes and coefficient of polynomial.​

Answer 1

Polynomials. Find the zeroes of a quadratic polynomial 5x2 – 4 – 8x and verify the relationship between the zeroes and the coefficients. Therefore, the zeroes of 5x2 – 8x – 4 are –2/5 and 2. ... (v) Graph y = p(x) cuts the x-axis at four points, so the given polynomial has 4 zeroes.

Answer 2

Your answer is:-

Let f(x) = 5x2 + 8x - 4 and α and β be its zeroes

Here a = 5, b = 8 and c = -4

5x2 + 8x - 4 = 0

5x2 + 10x - 2x - 4 = 0

5x(x + 2) - 2(x + 2) = 0

(x + 2)(5x - 2) = 0

x + 2 = 0 or 5x - 2 = 0

x = -2 or x= 2/5

So, the zeroes are α = -2 and β = 2/5

α + β = -2 + 2/5 = -8/5

-b/a = -8/5

So, α + β = -b/a

αβ = -2*2/5 = -4/5

c/a = -4/5

So, αβ = c/a