How do you find K with equal roots?

How do you find K with equal roots?

1 Answer

1. The given equation is (k – 12)x2 + 2(k – 12)x + 2 = 0.
2. Here, a = k – 12, b = 2(k – 12) and c = 2.
3. Since, the given equation has two equal real roots.
4. Then we must have b2 – 4ac = 0.
5. ⇒ {2(k – 12)}2 – 4(k – 12) × 2 = 0.
6. ⇒ 4(k – 12)2 – 8(k – 12) = 0.
7. ⇒ 4(k – 12) {k – 12 – 2} = 0.
8. ⇒ (k – 12)(k – 14) = 0.

When a quadratic equation has equal roots?

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.

For what value of k it has equal roots?

Complete step by step answer: 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} $ .

How do you find K in an equation?

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

For what value of k does the quadratic equation?

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 many roots are in quadratic equation?

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

What is K in a polynomial equation?

k is a zero of f(x) if and only if (x−k) is a factor of f(x) . Each rational zero of a polynomial function with integer coefficients will be equal to a factor of the constant term divided by a factor of the leading coefficient.

What is the K value in math?

The numeric value of K is approximately 2.6854520010.