Question

Assertion (A): The quadratic equation $$x^{2}-x-6=0$$ has –2 and 3 as its roots.

Reason (R): If $$ax^{2}+bx+c=0$$ then $$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}.$$

विकल्प

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. Here $$a=1,\ b=-1,\ c=-6.$$ Using the quadratic formula, $$x=\frac{1\pm\sqrt{1+24}}{2}=\frac{1\pm5}{2},$$ giving the roots $$3$$ and $$-2.$$

Step 2 – Reason: R is true. It is the quadratic formula for solving $$ax^{2}+bx+c=0.$$

Step 3 – Link: Substituting the equation’s coefficients into the formula gives the two roots stated in A.