If p and q are rational and q is not a perfect square, then the quadra

1.	If p and q are rational and q is not a perfect square, then the quadratic equation with rational coefficients whose one root is 5p - √q is 1. x2 -25px + 15p2 - q = 0 2. x2 +15px- q = 0 3. x2 -10px + 25q2 - p = 0 4. x2 -10px + 25p2 - q = 0
Answer» Correct Answer - Option 4 : x2 -10px + 25p2 - q = 0 Concept: Quadratic equation in the form of roots: x² – (sum of roots)x + product of roots = 0 In a quadratic equation surd or irrational roots occur in conjugate pairs. For example, if one of the roots of a quadratic equation is α + √β then the other root will be its conjugate that is α − √β Calculation: Here, one root is 5p - √q Since q is not a perfect square, therefore other root will be 5p +√q Now, required quadratic equation is x2 – (sum of roots)x + product of roots = 0 ⇒x² - (5p +√q + 5p - √q)x + (5p +√q)(5p -√q) = 0 ⇒ x² -10px + 25p² - q = 0 ⇒ x2 -10px + 25p² - q = 0 Hence, option (4) is correct.

If p and q are rational and q is not a perfect square, then the quadratic equation with rational coefficients whose one root is 5p - √q is 1. x2 -25px + 15p2 - q = 0 2. x2 +15px- q = 0 3. x2 -10px + 25q2 - p = 0 4. x2 -10px + 25p2 - q = 0

Answer» Correct Answer - Option 4 : x2 -10px + 25p2 - q = 0

Concept:

Quadratic equation in the form of roots: x² – (sum of roots)x + product of roots = 0

In a quadratic equation surd or irrational roots occur in conjugate pairs.

For example, if one of the roots of a quadratic equation is α + √β then the other root will be its conjugate that is α − √β

Calculation:

Here, one root is 5p - √q

Since q is not a perfect square, therefore other root will be 5p +√q

Now, required quadratic equation is x2 – (sum of roots)x + product of roots = 0

⇒x² - (5p +√q + 5p - √q)x + (5p +√q)(5p -√q) = 0

⇒ x² -10px + 25p² - q = 0

⇒ x2 -10px + 25p² - q = 0

Hence, option (4) is correct.