Question

without solving the following equation find the value of p for which the given equation has equal roots.
x^2+(p-1)x+(p+2)=0


the answer from book answer sheet is

7 or -1​

Answer 1

given that zeroes a=b

then 2a= -p-1 sum of the roots

a^2=p+2 product of he roots

Now, product of two numbers is 9=3×3

sum is 3+3=6

so, the value of p is 7

{or}

-1+2=1 or -1×-1=1

-1-1=-2 so, another value for p is -1

Answer 2

Answer:

The value of p is 7 or - 1.

Step-by-step-explanation:

The given quadratic equation is x² + ( p - 1 ) x + ( p + 2 ) = 0.

Compairing the given equation with ax² + bx + c = 0, we get,

x² + ( p - 1 ) x + ( p + 2 ) = 0

• a = 1
• b = ( p - 1 )
• c = ( p + 2 )

For real and equal roots,

b² - 4ac = 0

⇒ ( p - 1 )² - 4 * 1 * ( p + 2 ) = 0

⇒ ( p - 1 )² - 4 ( p + 2 ) = 0

⇒ p² - 2p + 1 - 4p - 8 = 0

⇒ p² - 2p - 4p - 7 = 0

⇒ p² - 6p - 7 = 0

⇒ p² - 7p + p - 7 = 0

⇒ p ( p - 7 ) + 1 ( p - 7 ) = 0

⇒ ( p - 7 ) ( p + 1 ) = 0

⇒ ( p - 7 ) = 0 OR ( p + 1 ) = 0

⇒ p - 7 = 0 OR p + 1 = 0

⇒ p = 7 OR p = - 1

∴ The value of p is 7 or - 1.