Question

Determine the set of values of p for which the given quadratic equation have real roots. (i) 5x²-2px+3​

Answer 1

Answer:

5x aga Tu solve kar le chvjvi Ghana uvyy

Answer 2

Answer:

$p$ ∈ $[\sqrt{15},$ ∞$)$; $p\geq \sqrt{15}$

Step-by-step explanation:

Given Quadratic equation:

$5x^{2} -2px+3 = 0$

Previous Knowledge:

We know that for a quadratic equation, of the form $ax^{2} +bx+c = 0$, has real roots when $b^{2} -4ac\geq 0$

To Find:

Values of $p$ for which the given equation has real roots

Solution:

The equation must have real roots

⇒ $b^{2} -4ac \geq 0$                                                         (Previous Knowledge)

⇒ $(-2p)^{2} -4(5)(3) \geq 0$

⇒ $4p^{2} -60 \geq 0$

Adding $60$ to both sides

⇒ $4p^{2} \geq 60$

Dividing by $4$ on both sides

⇒ $p^{2} \geq 15$

Rooting both sides

⇒ $p\geq \sqrt{15}$

In terms of Sets that means

$p$ ∈ $[\sqrt{15},$ ∞$)$