Question

Find the zeroes of the quadratic polynomial 5x2 + 8x – 4 and verify the relationship between the zeroes and the coefficients of the polynomial.

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Answer 1

Answer:

GivEn Quadratic Polynomial:

5x² + 8x - 4

We have to find,

Zeroes of polynomial and to verify the relationship between zeros and coefficient.

Solution:

Let's find zeroes of given polynomial,

⇏ 5x² + 8x - 4 = 0

⇏ 5x² + 10x - 2x - 4 = 0

⇏ 5x(x + 2) - 2(x + 2) = 0

⇏ (x + 2)(5x - 2) = 0

⇏ x = -2 or 2/5

∴ Two zeroes of given quadratic polynomial are -2 and 2/5.

Now,

We know that,

Sum of zeroes = - b/a

Product of zeroes = c/a

Here, In the given polynomial,

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

⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore,

Now, Sum of zeroes,

⇏ -2 + 2/5 = - 8/5

⇏ - 10 + 2/5 = - 8/5

⇏ - 8/5 = - 8/5

⇏ LHS = RHS

Hence, Verified!

Also, Product of zeroes,

⇏ (2/5) × (-2) = -4/5

⇏ - 4/5 = - 4/5

⇏ LHS = RHS

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Answer 2

Step-by-step explanation:

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

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