A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots iff these roots are both equal to the root of the derivative.

Which of the equation has equal 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. 1 The equation x2 + 3pq + p = 0, where is a non-zero constant, has equal roots.

What are two equal roots?

If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x² + 2x + 1. D > 0 means two real, distinct roots.

Where are the roots in a quadratic equation?

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax² + bx + c = 0.

When can be the roots of quadratic equation has real roots?

When a, b and c are real numbers, a ≠ 0 and discriminant is zero (i.e., b2 - 4ac = 0), then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and equal.

Equal Roots of a Quadratic Equation

24 related questions found

For what value of k the quadratic equation has equal roots?

For equal roots, the discriminant must be zero. Hence, the required values of k are 0 and 8.

Which quadratic equation has roots that are real numbers and equal?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax²+ bx + c = 0 are real and equal.

For what value of k does the quadratic have equal roots?

Hence, the values of K for the given quadratic equation to have equal roots are 2 and -2. Note: Here, it is important to note that a quadratic equation can have equal and real roots only when the discriminant of the quadratic equation is equal to zero.

How do you find K in a quadratic equation?

If you've already learned the Quadratic Formula, you may find it easy to memorize the formula for k, since it is related to both the formula for h and the discriminant in the Quadratic Formula: k = (4ac – b²) / 4a.

What is K in quadratic equation?

(h, k) is the vertex of the parabola, and x = h is the axis of symmetry. • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

For which value of k the quadratic equation 2x² KX k 0 has equal roots?

For equal roots, the discriminant must be zero. Hence the required values of k are 0 and 8.

What is real and unequal roots?

When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.

How do you tell if the roots are real rational and equal?

For real roots, we have the following further possibilities. If Δ=0, the roots are equal and we can say that there is only one root. If Δ>0, the roots are unequal and there are two further possibilities. Δ is the square of a rational number: the roots are rational.

How do you find real roots?

You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2x4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.

How many roots does a quadratic equation have?

A quadratic equation with real or complex coefficients has two solutions, called roots.

What is the quadratic equation if the roots are 2 and 3?

quadratic equation is x^2-5x+6.

Are complex and imaginary roots the same?

The roots belong to the set of complex numbers, and will be called "complex roots" (or "imaginary roots"). These complex roots will be expressed in the form a + bi.

What is equal root?

Hint: A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots iff these roots are both equal to the root of the derivative.

When to say that the roots of the quadratic equation is zero negative?

A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

For what value of k the roots of the quadratic equation 2k x2 KX 2 0 are equal?

Explanation: General format of quadratic equation is . c = constant term. Therefore, the values of k = 4 if roots are equal.

For what value of k does 2x2 KX 3 0 has equal roots?

Complete step by step answer:

Here, the given equation is $ 2{{x}^{2}}+kx+3=0 $ . Now, as mentioned above, for the equation to have equal roots, D=0. Thus, for the given equation to have equal roots, the value of k should be $ \pm 2\sqrt{6} $ .

For what value of k the equation Kx 2 6x 2 0 has real roots?

For what values of k, the equation kx^(2)-6x-2=0 has real roots? For real roots, we must have b2-4ac≥0. ⇒8k≥-36⇒k≥-92.