Question

If a and b are the zeros of the polynomial p(x) = 4x² + 3x + 7 then 1/a + 1/b = *

2 points

7/3

3/7

-7/3

-3/7

​

Answer 1

Step-by-step explanation:

Given: α,β are zeroes of the polynomial 4x

2

+3x+7

To find the value of

α

1

+

β

1

From the given quadratic equation,

α+β=−

4

3

and αβ=

4

7

Therefore,

α

1

+

β

1

=

αβ

α+β

=

4

7

−

4

3

=−

7

3

⇒

α

1

+

β

1

=− 7/3

Answer 2

let alpha and beta are the zeroes of the polynomial.

$\alpha + \beta = - b \div a \\ = - 3 \div 4 \\ \alpha \beta = c \div a \\ = 7 \div 4$

$so \\ 1 \div \alpha + 1 \div \beta =( \alpha + \beta ) \div \alpha \beta$

= (-3/4)÷(7/4)

-3/4×4/7

= -3/7

$therefore \: 1 \div \alpha + 1 \div \beta = - 3 \div 7$

HOPE IT HELPS!!!