Multiple Choice Questions

Let a and beta a gt beta be the roots of the equation x2 8x q 0 I...........

Mathematics (NDA) Quadratic Equations

Let a and β (a > β) be the roots of the equation x² - 8x + q = 0. If a² -β² = 16, then what is the value of q?

This questions was previously asked in

2022 NDA -1 Math

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- Given roots of the equation $x^{2} - 8 x + q = 0$ are $a$ and $ß$ .

- Using Vieta's formulas:

- The sum of roots $(a + ß) = 8$ .

- The product of roots $(a ß) = q$ .

- We know $a^{2} - ß^{2} = 16$ .

- This can be rewritten using the identity as $(a + ß) (a - ß) = 16$ .

- Substituting $a + ß = 8$ gives $8 (a - ß) = 16$ .

- So, $a - ß = 2$ .

- Solving the system:

- $a + ß = 8$

- $a - ß = 2$

- From these, $a = 5$ and $ß = 3$ .

- Using $a ß = q$ , we get $q = 5 \times 3 = 15$ .

- Hence, the correct option is Option: 4, 15.

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