Question

Factorise the following quadratic equation and find zeroes . Also verify the relationship between zeroes and coefficient .
1 . X square+8x+15=0

Answer 1

Answer:

Here is the answer

Answer 2

Zeroes of quadratic equation are -3, -5 and zeroes and coefficients are related to each other.

Step-by-step explanation:

We are given a quadratic equation,

$x^{2} +8x+15=0$

We have to find the zeroes of this equation and then compare them with coefficients.

Formula used

General quadratic equation is

$ax^{2} +bx+c=0$

Sum of zeroes of a quadratic equation  $=\frac{-b}{a}$

Product or zeroes of a quadratic equation $=\frac{c}{a}$

'a' is the coefficient of $x^{2}$ , 'b' is the coefficient of $x$ and 'c' is the constant.

• Calculation for Zeroes of quadratic equation

For finding zeroes of equation we use Factorization method here,

$x^{2} +8x+15=0$

we can write 8 as  $3+5$ and the multiplication of $3*5=15$ so,

$x^{2} +3x+5x+15=0$

taking common $x$ from first two terms and 5 from last two terms.

$x(x+3)+5(x+3)=0$

now taking $(x+3)$ common ,

$(x+3)(x+5)=0$

So the zeroes of equation are -3 and -5.

• Relation of zeroes and coefficients

We will find the sum of zeroes and product of zeroes from two methods. First by using zeroes itself and second by using formula of coefficients.

• By using zeroes,

let say first zero is $\alpha$ and second is $\beta$ so the

$\alpha =-3$  and $\beta =-5$

sum of zeroes $=\alpha +\beta$                               Product of zeroes$=\alpha *\beta$

                        $=-3+(-5)$                                                     $=(-3)*(-5)$

                        $=-8$                                                                 $=15$

• By using formula,

here in the given equation

$a=1,b=8$ and $c=15$

Sum of zeroes  $=\frac{-b}{a}$                    Product of zeroes $=\frac{c}{a}$              

                        $=\frac{-(8)}{1}$                                                    $=\frac{15}{1}$

                        $=-8$                                                      $=15$

Here we get  sum of zeroes and product of zeroes are same by both methods. So they are related to each other, Hence verified.