Question

determine the value of p for which the quadratic equation 2px^2+6x+5=0 has equal roots​

Answer 1

Answer:

p = 9/10

Step-by-step explanation:

2px²+6x+5=0

D = 36-4(2p)(5) = 0  {Discriminant of equal roots is 0}

0 = 36 - 40p

40p = 36

p = 36/40

p = 9/10

Answer 2

★ Given :

• Equation : 2px² + 6x + 5 = 0
• Equation has equal roots.

★ To Find :

We have to find the value of p.

★ Explanation :

As, it is given that the equation has equal roots. So, D must be zero in the discrimination formula.

$\large{\star{\underline{\boxed{\sf{D = b^2 - 4ac}}}}}$

$\sf{\dashrightarrow 0 = (6)^2 - 4(2p)(5)} \\ \\ \sf{\dashrightarrow 0 = 36 - 20(2p)} \\ \\ \sf{\dashrightarrow 0 = 36 - 40p} \\ \\ \sf{\dashrightarrow -36 = -40p} \\ \\ \sf{\dashrightarrow p = \dfrac{-36}{-40}} \\ \\ \sf{\dashrightarrow p = \dfrac{9}{10}}$

$\large{\star{\underline{\boxed{\sf{p = \dfrac{9}{10}}}}}}$