Question

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

Answer 1

please mark as brainliest answer.

Step-by-step explanation:

Let f(x) = 5x2 – 8x – 4

By splitting the middle term, we get

f(x) = 5x2 – 10x + 2x – 4

= 5x(x – 2) + 2(x – 2)

= (5x + 2) (x – 2)

On putting f(x) = 0 we get

(5x + 2) (x – 2) = 0

⇒ 5x + 2 = 0 or x – 2 = 0

x = -2/5 or x = 2

Thus, the zeroes of the given polynomialimage5x2 – 8x – 4 are -2/5 and 2

Answer 2

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

Hence, Verified!