Question

(ii) Determine the nature of the roots
of the quadratic equation
2x² - 3x - 4=0
​

Answer 1

Answer:

• Roots are imaginary.

Solution:

we know that,

$\large\red\boxed{D=b^2-4ac}$

• If D > 0 , then the roots are real and distinct .
• If D = 0 , then the roots are real and equal .
• If D < 0 , then the roots are imaginary.

Given Equation :

• 2x² - 3x - 4=0

​so here,

• a = 2

• b = -3
• c = -4

Now, find the discriminant of the equation

$\large\implies \sf D=b^2-4ac\\\\\large\implies\sf D = -3^2-4(2)(-4) \\\\\large\implies \sf D = 9-32 \\\\\large\implies\sf \boxed{\pink{ D=-23}}$

Here we got discriminant less than 0, D < 0.

Hence,

Roots are imaginary.