Question

determine the nature of roots of the quadratic equation 2 x square - 3 x minus 4 is equal to zero from is discriminant

Answer 1

Answer

DISCRIMINATE= -4ac


$\bftext{SOLUTION}$


$2 {x}^{2} - 3x - 4 = 0$

a=2,b=-3,c=-4


So



$\bftext{DISCRIMINATE}$=-4×2×(-4)

=32

it is positive so equation have. real and unequal root

NOW VALUE OF D

Case I: b2 – 4ac > 0


$\bftext{Explanation}$

When a, b, and c are real numbers, a ≠ 0 and discriminant is positive, then the roots α and β of the quadratic equation ax2 +bx+ c = 0 are real and unequal.


Case II: b2– 4ac = 0

$\bftext{Explanation}$


When a, b, and c are real numbers, a ≠ 0 and discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.


Case III: b2– 4ac < 0

$\bftext{Explanation}$


When a, b, and c are real numbers, a ≠ 0 and discriminant is negative, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.

Case IV: b2 – 4ac > 0 and perfect square

[tex]\bftex{Explanation}/[tex]

When a, b, and c are real numbers, a ≠ 0 and discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real, rational and unequal.


Case V: b2– 4ac > 0 and not perfect square

When a, b, and c are real numbers, a ≠ 0 and discriminant is positive but not a perfect square then the roots of the quadratic equation ax2 + bx + c = 0 are real, irrational and unequal.
Here the roots α and β form a pair of irrational conjugates.



Case VI: b2– 4ac >0 is perfect square and a or b is irrational



When a, b, and c are real numbers, a ≠ 0 and the discriminant is a perfect square but any one of a or b is irrational then the roots of the quadratic equation ax2 + bx + c = 0 are irrational.