Question

the discriminant of the following
2
$2x {}^{2} + 5 - 6$


1

48

-38

49​

Answer 1

GIVEN :-

• quadratic equation = 2x² + 5x - 6 .

TO FIND :-

• The discriminant of the quadratic equation.

SOLUTION :-

As we know that the discriminant of any quadratic equation is given by,

$\\ : \implies \displaystyle \sf \: Discriminant = b ^{2} - 4ac$

• a = 2.
• b = 5.
• c = -6.

$\\ \\ : \implies \displaystyle \sf \: Discriminant =5 ^{2} - 4 \times 2 \times ( - 6)$

$: \implies \displaystyle \sf \: Discriminant =25 - 8 \times ( - 6)$

$: \implies \displaystyle \sf \: Discriminant =25 - ( - 48)$

$: \implies \displaystyle \sf \: Discriminant =25 + 48$

$: \implies \underline{ \boxed{ \displaystyle \sf \: Discriminant =73}}$

Now let's find the roots of the given quadratic equation by using the quadratic formula,

$\\ \\ : \implies \displaystyle \sf \: x = \frac{ - b \pm \sqrt{b ^{2} - 4ac } }{2a}$

• a = 2.
• b = 5.
• c = -6.

$\\ \\ : \implies \displaystyle \sf \: x = \frac{ - 5 \pm \sqrt{5 ^{2} - 4 \times 2 \times ( - 6) } }{2 \times 2}$

$: \implies \displaystyle \sf \: x = \frac{ - 5 \pm \sqrt{25 - ( - 48)} }{4}$

$: \implies \displaystyle \sf \: x = \frac{ - 5 \pm \sqrt{25 + 48} }{4}$

$: \implies \displaystyle \sf \: x = \frac{ - 5 \pm \sqrt{73} }{4}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x = \frac{ - 5 + \sqrt{73} }{4} }}$

$: \implies \underline{ \boxed{\displaystyle \sf \: x = \frac{ - 5 - \sqrt{73} }{4} }}$

Answer 2

Given :

• A = 2

• B = 5

• C = - 6

To Find :

• what is the discriminant ?

Solution :

Concept :

• The Discriminant of the quadratic polynomial. It is zero if and only if the polynomial has a double root, and is positive if and only if the polynomial has two real roots.

$: \sf \implies \: \: \: \: D = {b}^{2} - 4 a c$

Substitute all values :

$: \sf \implies \: \: \: \: D = {5}^{2} - 4 \times 2 \times - 6\\ \\ \\ : \sf \implies \: \: \: \: D = 25 + 48 \\ \\ \\ : \sf \implies \: \: \: \: D = 73$