What is the discriminant if there are 2 real roots?

The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots.

How do you find two real roots of a quadratic equation?

For a quadratic equation ax2 + bx + c = 0,

  1. The roots are calculated using the formula, x = (-b ± √ (b² – 4ac) )/2a.
  2. Discriminant is, D = b2 – 4ac. If D > 0, then the equation has two real and distinct roots. If D < 0, the equation has two complex roots.
  3. Sum of the roots = -b/a.
  4. Product of the roots = c/a.

Can a quadratic equation have 2 roots?

We will discuss here that a quadratic equation cannot have more than two roots. Proof: Let us assumed that α, β and γ be three distinct roots of the quadratic equation of the general form ax2 + bx + c = 0, where a, b, c are three real numbers and a ≠ 0.

What is the discriminant if the quadratic equation has two real number solutions?

If the discriminant is greater than 0, the quadratic equation has 2 real solutions. If the discriminant is equal to 0, the quadratic equation has 1 real solution.

What does 2 equal roots mean?

When solving a quadratic equation for which the discriminant is zero (ie. b2−4ac=0) we say there are “two real and equal roots”.

What is discriminant in quadratic equation?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

Why a quadratic equation has 2 roots?

Except α and β no other values of x satisfies the equation ax2 + bx + c = 0. Hence, we can say that the equation ax2 + bx + c = 0 has two and only two roots. Therefore, a quadratic equation has two and only two roots.

Which of the following is the value of the discriminant for √ 2×2 5x+ √ 2 0?

Answer. the value of discriminant is 17.

How many real roots does the quadratic equation?

two roots
The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots.