Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients. 3x^2-x-4 ​

Answer 1

EXPLANATION.

Equation → 3x² - x - 4 = 0.

Sum of zeroes of quadratic equation

a + b = -b/a

a + b = 1/3.

Products of zeroes of quadratic equation

ab = c/a.

ab = -4/3.

Equation → 3x² - x - 4 = 0.

Factories into middle term split.

→ 3x² - 4x + 3x - 4 = 0.

→ x ( 3x - 4 ) + 1 ( 3x - 4 ) = 0.

→ ( x + 1 ) ( 3x - 4 ) = 0.

→ x = -1 and x = 4/3.

Products = -1 X 4/3 = -4/3.

Sum = -1 + 4/3 = 1/3.

HENCE PROVED.

Answer 2

Answer :-

Given :-

• Quadratic equation → 3x² - x - 4 = 0

Calculating zeros :-

By middle term splitting method -

→ 3x² - x - 4 = 0

→ 3x² + 3x - 4x - 4 = 0

→ 3x ( x + 1 ) - 4 ( x + 1 ) = 0

→ ( 3x - 4 )( x + 1 ) = 0

When ( 3x - 4 ) = 0

→ 3x - 4 = 0

→ 3x = 4

→ x = 4/3

When ( x + 1 ) = 0

→ x + 1 = 0

→ x = -1

Zeros = 4/3 , -1

Relationship between zeros and the coefficients -

• a = 3
• b = -1
• c = -4

Sum of zeros = - b/a = 1/3

Product of zeros = c/a = -4/3

Verification :-

Sum of zeros = 4/3 + ( -1 ) = 1/3

Product = 4/3 × (-1) = -4/3

• 1/3 = 1/3
• -4/3 = -4/3

Hence verified.