Question

2*x*x+x-1 state whether the quadratic equation have two distinct real roots or not

Answer 1

Given :-

2x² + x - 1

Here, we've to state whether the quadratic equation has two distinct real roots or not.

We can either solve it and can find or we can take the help of D (discriminate)

If the D is positive, then the quadratic equation has two distinct and real roots.

Two distinct and real roots.if the D is 0, then the quadratic equation has 2 equal roots.

2 equal roots.if the D is negative, then it has no real roots.

D = b² - 4ac

We know the standard form of a quadratic equation. that's ax² + bx + c

Here a = 2, b = 1 and c = -1

➡ D = (1)² - 4(2)(-1)

= 1 - (-8)

= 1 + 8

= 9

D is positive. hence it has 2 distinct real roots.

Answer 2

$\huge{\mathfrak{Answer :-}}$

$\large{\bf{Given :-}}$

2x² + x - 1

$\large{\bf{To \:\:Find :-}}$

$\large{\sf{Equation\:\:have \:\: two \:\:distinct\:\: roots \:\:or\:\:not.}}$

$\huge{\bf{A.T.Q}}$

$\huge{\bf{By\:\:quadratic\:\:formula}}$

D = b² - 4ac

$\large{\sf{D = (1) - 4(2)(-1)}}$

$\large{\sf{D = 1 -(-8)}}$

$\large{\sf{D = 1 + 8}}$

$\large{\sf{D = 9}}$

$\huge{\boxed{D = 9}}$

$\huge{\bf{It\:\: has\:\: equal\:\: and \:\:distinct \:\:roots\:\: because\:\: D\:\: is\:\: positive.}}$