Question

The quadratic equation is:x^2+px-q=0 n the roots are 1 and -5. Find the values of p and q?

Answer 1

❥${\red{\underline{\underline{\huge{\mathtt{Question:-}}}}}}$

The quadratic equation is:x²+px-q=0 and the roots are 1 and -5. Find the values of p and q?

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

• Given that the roots are 1 and -5 of the quadratic equation.

★${\green{\bold{Equation→}}}$ x²+px-q=0

✞Putting x=1 in the given equation✞

x²+px-q=0

→1² +p×1-q=0

→1+p-q =0

→p-q= -1......................(i)

✞ Putting x = -5 in the given equation✞

x²+px-q=0

→(-5)²+p(-5)-q=0

→25 -5p -q =0

→ -5p-q=-25

→ 5p+q = 25....…...........(ii)

★${\purple{\bold{By\: elimination:-}}}$

p-q= -1

5p+q=25

___________

6p=24

→ p = 4

ᴥ${\orange{\boxed{\boxed{\large{\bold{p\:=\:4}}}}}}$

† Putting p = 4 in the (i) no. equation†

p - q = -1

→4 - q = -1

→-q = -5

→ q = 5

ᴥ${\orange{\boxed{\boxed{\large{\bold{q\:=\:5}}}}}}$

❥${\red{\underline{\underline{\huge{\mathtt{Answer:-}}}}}}$

•Value of p is 4.

•Value of q is 5.