What is the condition for common root in quadratic equation?

What is the condition for common root in quadratic equation?

Consider two quadratic equations a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0. Let α be the root that is common in the quadratic equations. If both roots are common, then the condition is (a1 / a2) = (b1 / b2) = (c1 / c2).

What is the condition for one root of the quadratic equation is reciprocal of the other?

Answer: Since one solution is the reciprocal of the other, we have r1r2=1, so that a=c. Hence, the roots are reciprocals of one another only when a=c. By the Quadratic Formula, given ax2+bx+c=0 with a≠0, we have x=−b±√b2−4ac2a.

What is meant by common root?

In traditional root words, these words come from Latin and Greek, and typically do not stand alone as a complete word. Understanding the meanings of common roots can help you work out the meanings of new words as you encounter them. For example, “egotist” has a root word of “ego” plus the suffix -ist.

How do you take common roots?

Condition for one common root: ⇒ (c1a2 – c2a1)^2 = (b1c2 – b2c1)(a1b2 – a2b1), which is the required condition for one root to be common of two quadratic equations. Note: (i) We can find the common root by making the same coefficient of x^2 of the given equations and then subtracting the two equations.

What if roots are reciprocal?

The product of these reciprocal roots is 1/p * 1/q = A / C. The sum of these reciprocal roots is 1/p + 1/q = -B / C. If the sum and product of roots is known, the quadratic equation can be x2 – (Sum of the roots)x + (Product of the roots) = 0.

What is the condition that one root of the quadratic equation AX² bx c 0 is reciprocal of the other * 1 point?

The roots of the equation ax^(2)+bx+c=0 will be reciprocal of each other if. Product of roots =ca. Also,(α×1α)=1.

How do I find the root of one root?

Now, we can find the other root by the formula for sum and product of the roots. If $\alpha$ and $\beta$ are the two roots of the quadratic equation $a{{x}^{2}}+bx+c=0$ then the sum and product of the roots are given by the formula: $\alpha +\beta =\dfrac{-b}{a}$ and $\alpha \beta =\dfrac{c}{a}$.