Question

Find the zeroes of following quadratic
polynomials and verify the relationship between
be zero and cofficients . 3x square-x- 4
​

Answer 1

Answer:

3x²-x - 4

=> 3x²+3x-4x - 4

=> 3x ( x + 1) - 4(x +1)

=> (3x - 4) (x + 1)

=> x = 4/3 , x = -1

Relationship be zero and cofficients

Sum of zeroes => -b/ a Or 4/3 + (-1/1

=> -(-1) /3 => 1/3 or 1/3

Product of zeros => c/a => -4/3 Or 4/3 × (-1) => -4/3

Answer 2

Answer:

The relationship between zeros and coefficients is verified.

Step-by-step explanation:

Find the zeros,

$\longrightarrow$ 3x² - x - 4

$\longrightarrow$ 3x² + 3x - 4x - 4

$\longrightarrow$ 3x(x + 1) - 4(x + 1)

$\longrightarrow$ (3x - 4)(x + 1)

Zeros,

$\longrightarrow$ x + 1 = 0

$\longrightarrow$ x = -1

$\longrightarrow$ 3x - 4 = 0

$\longrightarrow$ 3x = 4

$\longrightarrow$ x = 4/3

Zeros are -1 and 4/3.

So, let α and β be (-1) and 4/3.

_________________________

Verifying the relationship between zeros and coefficients.

In the polynomial,

• a = 3
• b = (-1)
• c = (-4)

________________________

★ Sum of zeros:

$\longrightarrow$ 4/3 + (-1)

$\longrightarrow$ 4/3 - 3/3

$\longrightarrow$ (4 - 3)/3

$\longrightarrow$ 1/3 ---- (I)

$\longrightarrow$ α + β = -b/a

$\longrightarrow$ α + β = -(-1)/3

$\longrightarrow$ α + β = 1/3 ---- (II)

_________________________

★ Product of zeros:

$\longrightarrow$ 4/3 × (-1)

$\longrightarrow$ -4/3 ---- (III)

$\longrightarrow$ αβ = c/a

$\longrightarrow$ αβ = -4/3 ---- (IV)

I and II are equal. III and IV are equal.

Hence, the relationship between zeros and coefficients is verified.