Question

Find the discriminant of the following quadratic equation and hence find the nature of roots :

4x^2 – 5x + 1 = 0.​

Answer 1

Answer:

Given :-

• The quadratic equation is 4x² - 5x + 1 = 0.

To Find :-

• What is the discriminate and the náture of the roots.

Formula Used :-

$\clubsuit$ Discriminate Formula :

$\longmapsto \sf\boxed{\bold{\pink{Discriminate\: (D) =\: b^2 - 4ac}}}$

Solution :-

Given equation :

$\leadsto \sf\bold{\purple{4x^2 - 5x + 1 =\: 0}}$

where,

■ a = 4

■ b = - 5

■ c = 1

According to the question by using the formula we get,

$\longrightarrow \sf Discriminate\: (D) =\: (- 5)^2 - 4(4)(1)$

$\longrightarrow \sf Discriminate\: (D) =\: (- 5)(- 5) - 4 \times 4 \times 1$

$\longrightarrow \sf Discriminate\: (D) =\: 25 - 16 \times 1$

$\longrightarrow \sf Discriminate\: (D) =\: 25 - 16$

$\longrightarrow \sf\bold{\red{Discriminate\: =\: 9 > 0}}$

$\therefore$ The discriminate is 9.

$\therefore$ The roots are real, rational and unequal.

EXTRA INFORMATION :-

❒ The general form of equation is ax² + bx + c = 0 then the equation becomes to a linear equation.

[ Note : ● If b = 0 then the roots of the equation becomes equal but opposite in sign.

● If c = 0 then one of the roots is zero. ]