Question

Read the question in the picture .

Answer 1

Answer:

Rational , they are -1 and 4/10

Answer 2

Answer:

Given :

Quadratic Equation

$5 {x}^{2} + 3x - 2 = 0$

What to find out = nature of the roots?

Solution :

Factorise the equation by splitting the middle term

$5 {x}^{2} + 3x - 2 = 0 \\ = 5 {x}^{2} + 5x - 2x - 2 = 0 \\ = 5x(x + 1) - 2(x + 1) = 0 \\ = (x + 1)(5x - 2) = 0 \\ = x = - 1 \: \: and \: \: \frac{2}{5} \: \:$

Or use discriminant method

Formula

$d {}^{2} = b {}^{2} - 4ac$

Where b= 3, a=5 and c= (-2)

Hence,

$d {}^{2} = 3 {}^{2} - 4 \times 5 \times ( - 2) \\ d {}^{2} = 49 \\ as \: d > 0 \\ hence \: the \: qudratic \: equation \: has \: two \: real \: roots.$

Hence option (3) is correct option.

Extra :✈

Question :How to know a quadratic equation has real roots?

Answer :For an equation ax2+bx+c = 0, b2-4ac is called the discriminant and helps in determining the nature of the roots of a quadratic equation. If b2-4ac > 0, the roots are real and distinct. If b2-4ac = 0, the roots are real and equal.