Question

24. If 2, B are the zeros of the polynomial P(x) = 4x²+3x+7
then a/b+ 1/b is equal to.​

Answer 1

Answer:

If a and b are zeroes of the polynomial p(x) = $4x^{2} +3x-7$, then the value of a/b+ 1/b is $\frac{-8}{7}$.

Step-by-step explanation:

$P\left( x\right) =4x^{2}+3x-7$

To determine the values of its zeroes, we have to equate it with zero.

$4x^{2}+3x-7=0$

Factorizing the polynomial now equated with zero

$4x^{2} - 4x +7x+7=0$

$4x(x-1)+7(x-1)=0$

$(x-1)(4x+7)=0$

Therefore,

$x-1=0\\x=1$

Or

$4x+7=0\\x=\frac{-7}{4}$

Hence the two zeroes of the polynomial p(x) = $4x^{2} +3x-7$ are

a = 1 and

b = $\frac{-7}{4}$.

From the above values,

$\frac{a}{b} = 1/ \frac{-7}{4}$

$\frac{a}{b} = \frac{-4}{7}$

and

$\frac{1}{b} = \frac{-4}{7}$

$\frac{a}{b}+ \frac{1}{b} = \frac{-4}{7}+ \frac{-4}{7}$

∴ $\frac{a}{b} +\frac{1}{b} = \frac{-8}{7}$

is the required value.