Question

Find the zeroes of the polynomial

p( x ) = x² + 7x + 10 and verify the relationship between the zeroes and coefficients.

Answer 1

hope it will help u...☺

Answer 2

Answer:  Zeroes of the polynomial is -5 and -2.

Step-by-step explanation:

Since we have given that

$p(x)=x^2+7x+10$

We need to first "Split the middle term and get the required roots":

$x^2+7x+10=0\\\\x^2+5x+2x+10=0\\\\x(x+5)+2(x+5)=0\\\\(x+5)(x+2)=0\\\\x=-5,-2$

So, we get that

$\alpha=-5,\beta=-2$

Now, we know the relationships between the zeroes and coefficients.

The standard form of quadratic form is :

$x^2-(\alpha+\beta)x+\alpha \beta=0\\\\So,\\\\\alpha+\beta=-5-2=-7=\frac{-b}{a}=\frac{-7}{1}=-7\\\\\alpha \beta=-5\times -2=10=\frac{c}{a}=\frac{10}{1}=10$

Therefore, Zeroes of the polynomial is -5 and -2.

Hence, verified.