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.