Can two roots of a quadratic equation have k=0?

We know that two roots of quadratic equation are equal only if discriminant is equal to zero. Putting discriminant equal to zero, we get. The basic definition of quadratic equation says that quadratic equation is the equation of the form , where . Therefore, in equation , we cannot have k =0.

How do you find the value of K in a quadratic equation?

Let one root of the quadratic equation x^2 – x – k = 0 be square of the other. Then find the value of k . Let one root of the quadratic equation x2 −x−k = 0 be square of the other. Then find the value of k. Let the roots of the quadratic equation x2−x−k = 0 be α,α2. α+α2 = 1 …… (1) and α3 = −k …… (2).

How do you solve Ax^2}+bx+c=0 using quadratic formula?

Divide x ( 2 − x) by − 2 + x. All equations of the form ax^ {2}+bx+c=0 can be solved using the quadratic formula: \\frac {-b±\\sqrt {b^ {2}-4ac}} {2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

How do you know if an equation has two real roots?

Here, a=-3, b=2, and c=1 So, by plugging the values into the formula we get: Once you plugged the values of a, b, and c, you have to simplify the values in the equation. From the previous example, you have: If the value is positive, then equation has two real roots.

How do you find the product of the roots of quadratic equations?

If α and β are the two roots of a quadratic equation, then the formula to construct the quadratic equation is x 2 – (α + β)x + α β = 0. That is, x 2 – (sum of roots)x + product of roots = 0. If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of x 2, x and constant term.

How to find the root of a quadratic equation with opposite sign?

The roots of quadratic equation are equal in magnitude but of opposite sign if b = 0 and ac < 0; The root with greater magnitude is negative if the sign of a = sign of b × sign of c; If a > 0, c < 0 or a > 0, c > 0; the roots of quadratic equation will have opposite sign; If y = ax 2 + bx + c is positive for all real values of x, a > 0 and D < 0

What are the roots of x2 + px + q = 0?

If α and β be the roots of x2 + px + q = 0, find the quadratic equation whose roots are Given : α and β be the roots of x2 + px + q = 0. Find the value of (α/β + β/α).

How do you find the beta of a quadratic equation?

Find the quadratic equation with roots α and β given α − β = 2 and α 2 − β 2 = 3. We’ll set up a system of two equations in two unknowns to find `alpha` and `beta`. Since ` (alpha + beta) = 3/2` then `beta = 3/2 – alpha`, giving us `beta = -1/4`.

What is the root of x2 + Kx + 3 = 0?

The equation x2 + kx + 3 = 0, where k is a constant, has no real roots. Find the set of possible values of k, giving your answer in surd form.

What is the product of the roots Alpha and beta?

`alpha + beta = -b/a` The product of the roots `alpha` and `beta` is given by: `alpha beta = c/a` It’s also important to realize that if `alpha` and `beta` are roots, then: `(x-alpha)(x-beta)=0` We can expand the left side of the above equation to give us the following form for the quadratic formula: `x^2 – (alpha+beta)x + alpha beta = 0` Let’s