Q5 of 51 Page 38

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rational? Justify.

Yes, a quadratic equation whose coefficients are irrational can have rational roots.

Example: Consider the following equation,



The roots of the given equation are 4 and 1 which are rational.


More from this chapter

All 51 →
3

A quadratic equation with integral coefficient has integral roots. Justify your answer.

 4

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

 6

Is 0.2 a root of the equation x2 - 0.4 = 0? Justify your answer.

 7

If b = 0, c < 0, is it true the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify your answer.