Question

In x²+7x+5=0, is it possible to solve the equation by extracting the square root method or by factoring method? Explain your answer in 2 sentences.

Answer 1

if we  multiply 2 to 5 then we  find its lcm  we will easily  get the answer.

it is easy as those are linear equation.

Answer 2

Given:

A quadratic equation x²+7x+5=0.

To Find:

The roots of the equation by factorizing method or square root method.

Solution:

The given question can be solved using the concepts of quadratic equations.

1. Consider a quadratic equation a²+bx+c=0. The discriminant of any quadratic equation is given by the formula$\sqrt{b^{2}-4ac }$.

2. If the value of the discriminant is greater than 0, the roots are real and they are distinct.

3. If the value of the discriminant is equal to 0, the roots are real and they are equal.

4. If the value of the discriminant is less than 0, the roots are imaginary.

=> Discriminant of x²+7x+5=0 is$\sqrt{49-20}=\sqrt{29}$,

=> Roots of the given equation are real and distinct.

5. The roots of the given equation cannot be found by squaring method or factorizing method since the roots are not integral values.

6. In such cases we use the formula for finding the roots of the quadratic equation.

=> Roots of the given equation = $\frac{-7+\sqrt{29}}{2} , \frac{-7-\sqrt{29}}{2}$ which are rational values.

7. Since the roots are irrational, it is not possible to find the roots using the factorization method.

Therefore, it is not possible to find the roots using factorization or the square root method.