Question

Find the zeroes of P(x) = x² – 15 and find the relationship between zeroes and

coefficients.​

Answer 1

Given

We have given p(x)= x²-15

To Find

We have to find the zeroes and hence find the relationship between it's zeroes and it's coefficients

$\sf\huge {\underline{\underline{{Solution}}}}$

Finding zeroes of the given equation

=> x²-15

=>x²-15=0

Adding +15 and -15 to both sides

=> x²-15+15= 15-15+15

=>x²=15

x= ±√15

We obtain two zeroes : √15 & -√15

Finding the relationship between zeroes and coefficients:

Let us assume the two zeroes be λ & β

Sum of zeroes = -b/a

=> λ + β= -b/a

=> √15-√15= -0/1

0= 0----------(1)

Product of its zeroes

=>λ β= c/a

=> √15*-√15= -15/1

=> -15= -15 ---------(2)

Since,both Equation 1 and Equation are equal

Hence, relationship between the zeroes and coefficients is verified.

Answer 2

Step-by-step explanation:

Given

We have given p(x)= x²-15

To Find

We have to find the zeroes and hence find the relationship between it's zeroes and it's coefficients

$\sf\huge {\underline{\underline{{Solution}}}} </p><p>Solution</p><p>$

Finding zeroes of the given equation

=> x²-15

=>x²-15=0

Adding +15 and -15 to both sides

=> x²-15+15= 15-15+15

=>x²=15

x= ±√15

We obtain two zeroes : √15 & -√15

Finding the relationship between zeroes and coefficients:

Let us assume the two zeroes be λ & β

Sum of zeroes = -b/a

=> λ + β= -b/a

=> √15-√15= -0/1

0= 0----------(1)

Product of its zeroes

=>λ β= c/a

=> √15*-√15= -15/1

=> -15= -15 ---------(2)

Since,both Equation 1 and Equation are equal

Hence, relationship between the zeroes and coefficients is verified.