Question

if the quadratic equation px square minus 2 root 5 x + 15 equal to zero has two equal roots then find the value of p​

Answer 1

AnsWer :

1/3.

Solution :

We have, Quadratic Equation.

$\tt \dagger \: \: \: \: \: p {x}^{2} -2\sqrt{ 5}x + 15 =0 .$

Compare with General Equation.

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c = 0. \\ \tt \dagger \: \: \: \: \: \red{ a \neq0.}$

• a = p.
• b = - 2√5.
• c = 15.
• There both roots are equal.
• D = 0.

$\tt \dagger \: \: \: \: \: D = {b}^{2} - 4ac.$

Here,

• D ( Discriminate )

★ A/Q,

$\tt : \implies D = {b}^{2} - 4ac.$

$\tt : \implies D = { \big(2\sqrt{5} \big)}^{2} - 4 \times p \times 15$

$\tt : \implies D = 20 - 60p$

• Given ( D = 0 )

So,

$\tt : \implies 0 = 20 - 60p.$

$\tt : \implies - 20 = - 60p.$

$\tt : \implies 20 = 60p.$

$\tt : \implies \dfrac{20}{60} = p.$

$\tt : \implies \dfrac{1}{3} = p.$

Therefore, the value of P is 1/3.