Question

nature nature root of the quadratic equation : 2x² -3x+2=0​

Answer 1

$\large \underbrace{\bf {\pink {Question:-}}}$

Find the nature of the roots of the quadratic equation : $\sf 2x^2-3x+2=0$

$\large \underbrace{\bf{\pink{Solution:-}}}$

• We are given a quadratic equation $\sf 2x^2-3x+2=0$.
• We have to find the nature of the roots
• For this, we shall have to find the discriminant of the equation.

$\underline{\pmb{\sf{\green{→~~Discriminant = b^2-4ac}}}}$

Here, in the equation $\sf 2x^2-3x+2=0$,

• a = 2
• b = -3
• c = 2

Now, we'll substitute these formulas and solve :

$\sf {\green{→~~Discriminant = b^2-4ac}}$

$\sf {\green{→~~Discriminant= (-3)^2-4(2)(2)}}$

$\sf {\green {→~~Discriminant = 9-16}}$

$\sf {\green {→~~ Discriminant = -7}}$

Here, the discriminant < 0.

So, by this, we can conclude that the roots of this quadratic equation are imaginary [not real].

Answer 2

Given :-

• 2x² + 3x + 2 = 0

To Find :-

• What is the nature of roots of the quadratic equation.

Formula Used :-

$\clubsuit$ Discriminant Formula :

$\begin{gathered}\mapsto \sf\boxed{\bold{\purple{Discriminant\: (D) =\: b^2 - 4ac}}}\\\end{gathered}$

Solution :-

Given Equation :

$\implies \sf \bold{\purple{2x^2 + 3x + 2 =\: 0}}$

where,

• a = 2
• b = 2
• c = 2

According to the question by using the formula we get,

$\sf {\ {→Discriminant = b^2-4ac}}$

$\sf {\ {→Discriminant= (-3)^2-4(2)(2)}}$

$\sf {\ {→Discriminant = 9-16}}$

$\sf {\ {→Discriminant = -7<0}}$

∴ The nature of roots of the quadratic equation is real, irrational and distinct.

Hence, the correct options is option no (a) Real, irrational and distinct.

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃