Question

without solving the equation find the nature of the roots of the quadratic equation √2x²-5√3+2√2​

Answer 1

Answer:

I hope it helps!!

(I think you forgot to type x with 5√3)

Answer 2

Correct Question

Without solving the equation, find the nature of the roots of the quadratic equation $\sqrt{2}x^2 - 5 \sqrt{3}x + 2 \sqrt{2}$.

Solution

What we can observe?

From the given equation, we can observe that,

$\implies a = \sqrt{2}$

$\implies b = -5 \sqrt{3}$

$\implies c = 2 \sqrt{2}$

Discriminant

Discriminant of a quadratic equation tells us or determines the nature of roots. It is usually denoted by the formula $D = b^2 - 4ac$.

Nature of roots

$\implies D = b^2 - 4ac$

$\implies D = (-5 \sqrt{3})^2 - (4 \times \sqrt{2} \times 2 \sqrt{2})$

$\implies D = 75 - 16$

$\implies{\boxed{D = 59}}$

Since Discriminant is greater than 0, the nature of roots are real and distinct.

More Information

The quadratic equation $ax^2+bx+c = 0$ has:

(i) two distinct real roots, if $D = b^2 - 4ac$ is greater than $0$

(ii) two equal real roots i.e. coincident real roots if $D = b^2 - 4ac = 0$

(iii) no real roots, if $D = b^2 - 4ac$ is lesser than $0$

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