Table of Contents

## How do you find the other roots of a quadratic equation if one root is given?

If a quadratic equation has two real equal roots α, we say the equation has only one real solution. So, x = -1 is a root of the quadratic equation 3×2 + x – 2 = 0. Similarly, x = 2/3 is another root of the equation.

**Can a quadratic equation have one root rational and other root irrational?**

Yes, a pretty straightforward question.

**How do you find the other root when one is given?**

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 $\alpha \beta =\dfrac{c}{a}$.

### How many roots are there in quadratic equation?

two roots

The quadratic equation will always have two roots. The nature of roots may be either real or imaginary. A quadratic polynomial, when equated to zero, becomes a quadratic equation. The values of x satisfying the equation are called the roots of the quadratic equation.

**Which of the quadratic 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.

**Can a quadratic equation Cannot have irrational roots?**

(iii) From Case IV and Case V we conclude that the quadratic equation with rational coefficient cannot have only one rational and only one irrational roots; either both the roots are rational when b2 – 4ac is a perfect square or both the roots are irrational b2 – 4ac is not a perfect square.

## Can quadratic equation have irrational roots?

In a quadratic equation with rational coefficients has a irrational or surd root α + √β, where α and β are rational and β is not a perfect square, then it has also a conjugate root α – √β.

**What is AB and c in the quadratic formula?**

MathHelp.com. Practice The Quadratic Formula. The Quadratic Formula uses the “a”, “b”, and “c” from “ax2 + bx + c”, where “a”, “b”, and “c” are just numbers; they are the “numerical coefficients” of the quadratic equation they’ve given you to solve.

**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.

### What is the other root of a quadratic equation with one root?

So, the other root of a quadratic equation having the one root as (a+√b) is (a-√b), where a and b are rational numbers. , Ph.D.

**How do you find the rational numbers of a quadratic equation?**

Suppose the given quadratic equation is px² + qx + r= 0, where a , b and c are rational numbers. If α and β are two roots of the above equation with α = a+√b. Now α + β = -q/p, which is rational.

**Is it possible for a quadratic equation to have two solutions?**

Yes, a pretty straightforward question. Is it possible? has two solutions, namely x = 0 (which is rational) and x = 2 (which is irrational). However, if we only allow rational coefficients for our quadratic equation, then it is true that either both solutions are rational or both are irrational.

## Is X^2-sqrt{2}x=0} rational or irrational?

Yes; for example, the quadratic equation $$x^2-sqrt{2}x=0$$ has two solutions, namely $x=0$ (which is rational) and $x=sqrt{2}$ (which is irrational). However, if we only allow rational coefficientsfor our quadratic equation, then it is true that either both solutions are rational or both are irrational.