Question

If √5 and -√5 are the roots of the equation 25x² + px + q = 0, then the values of p and q are respectively​

Answer 1

sum of root:- -b/a

so

0 = -p/25

and

p =0

PRODUCT OF ROOT :- C/A

so

-5 =Q/25

Q= -125

Answer 2

Answer:

The value of p and q are - 25√5 and 0 respectively.

Step-by-step-explanation:

The given quadratic equation is 25x² + px + q = 0.

We have given that, √5 & - √5 are roots of the quadratic equation.

We have to find the values of p and q.

By substituting x = √5 in the given equation, we get,

25x² + px + q = 0

⇒ 25 ( √5 )² + p * √5 + q = 0

⇒ 25 * 5 + √5 p + q = 0

⇒ 125 + √5 p + q = 0

⇒ q = - 125 - √5 p - - - ( 1 )

Now, by substituting x = - √5 in the equation, we get,

25x² + px + q = 0

⇒ 25 ( - √5 )² + p * ( - √5 ) + q = 0

⇒ 25 * ( - 5 ) - √5p + q = 0

⇒ - 125 - √5p + ( - 125 - √5 p ) = 0 - - - [ From ( 1 ) ]

⇒ - 125 - √5p - 125 - √5p = 0

⇒ - 250 - 2√5p = 0

⇒ 2 ( - 125 - √5p ) = 0

⇒ - 125 - √5p = 0

⇒ - √5p = 125

⇒ - p = 125 / √5

⇒ - p = ( √5 * √5 * 25 ) / √5

⇒ - p = 25√5

⇒ p = - 25√5

Now, by substituting this value in equation ( 1 ), we get,

q = - 125 - √5 p - - - ( 1 )

⇒ q = - 125 - √5 ( - 25√5 )

⇒ q = - 125 + ( 25 * 5 )

⇒ q = - 125 + 125

⇒ q = 0

∴ The value of p and q are - 25√5 and 0 respectively.