Question

find the discriminant quadratic equation
$\sqrt{5x { }^{2} } - 7x + 2 \sqrt{5 = 0}$
​

Answer 1

In a quadratic equation,

$D = b^2 - 4ac$.

By comparing $\sqrt{5} x^2 - 7x + 2 \sqrt{5} = 0$ with $ax^2 + bx + c = 0$ (standard form of quadratic equation), we got:-

• $a = \sqrt{5}$
• $b = - 7$
• $c = 2 \sqrt{5}$.

So, D = (- 7)² - 4(√5)(2√5)

=> D = 49 - 40 = + 9 (real number - answer).

More:-

What does the D imply here?

The value of D here is a real number but ≠ 0, so it will have two postive, distinct roots.

Apart from that,

The vertex of the parabola of any quadratic equation will be at $(- \dfrac{b}{2a}), (- \dfrac{D}{4a})$. Now you can calculate the vertex of the above equation!