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Answer 1

Given :-

4x² - x - 5

To Find :-

Zeroes of following quadratic polynomials and verify the relationship between the zeroes and the co-effecient

Solution :-

4x² - x - 5

By discrimination method

x = -b ± √(b² - 4ac)/2a

x = -1 ± √[1 - (4)(4)(-5)]/2(4)

x = -1 ± √[1 - (-80)]/8

x = -1 ± √[1 + 80]/8

x = -1 ± √[81]/8

x = -1 ± 9/8

Either

x = 1

or

x = -5/4

Verification

α + β = -b/a

1 + -5/4= -(1)/4

4 - 5/4 = -1/4

-1/4 = -1/4

Now,

αβ = c/a

1 × -5/4 = -5/4

-5/4 = -5/4

Answer 2

Answer

Zeroes are 5/4 and -1

Step-by-step explanation:

Given Quadratic equation → 4x² - x - 5

For finding the zeroes of a quadratic equation first find 2 numbers such that:

• Their product is -20
• Their sum is -1

The 2 numbers which satisfies these conditions are:

4 and -5

Now, factorise it by splitting the middle term.

4x² - x - 5 = 0

→ 4x² + 4x - 5x - 5 = 0

→ 4x (x + 1) - 5 (x + 1) = 0

→ (4x - 5) (x + 1) = 0

So,

• (4x - 5) = 0 → x = 5/4
• (x + 1) = 0 → x = -1

So, the factors are 5/4 and -1

Finding the sum of Zeroes:

α + β = -b/a

→ α + β = 1/4

→ 5/4 - 1 = 1/4

→ 5/4 - 4/4 = 1/4

→ 1/4 = 1/4

Hence, the sum of Zeroes are verified.

Finding the product of zeroes:

αβ = c/a

→ αβ = -5/4

→ 5/4 × -1 = -5/4

→ -5/4 = -5/4

Hence the product of zeroes are verified.