Factorise the following quadratic equation and find zeroes . Also verify the relationship between zeroes and coefficient .
1 . X square+8x+15=0
Answers
Answer:
Here is the answer
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,
We have to find the zeroes of this equation and then compare them with coefficients.
Formula used
General quadratic equation is
Sum of zeroes of a quadratic equation
Product or zeroes of a quadratic equation
'a' is the coefficient of , 'b' is the coefficient of and 'c' is the constant.
- Calculation for Zeroes of quadratic equation
For finding zeroes of equation we use Factorization method here,
we can write 8 as and the multiplication of so,
taking common from first two terms and 5 from last two terms.
now taking common ,
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 and second is so the
and
sum of zeroes Product of zeroes
- By using formula,
here in the given equation
and
Sum of zeroes Product of zeroes
Here we get sum of zeroes and product of zeroes are same by both methods. So they are related to each other, Hence verified.