Question

The equation ( k x^{2}+4 k x-1=k ) has two real, distinct roots. (a) Find the set of possible values for ( k ). (b) Consider the case when ( k=3 ). The roots of the equation can be expressed in the form ( p pm frac{q}{sqrt{3}} ), where ( p, q in mathbb{Z} ). Find the value of ( p ) and of ( q ).

          The equation ( k x^{2}+4 k x-1=k ) has two real, distinct roots.
(a) Find the set of possible values for ( k ).
(b) Consider the case when ( k=3 ). The roots of the equation can be expressed in the form ( p pm frac{q}{sqrt{3}} ), where ( p, q in mathbb{Z} ). Find the value of ( p ) and of ( q ).

$The equation ( k x^2+4 k x-1=k ) has two real, distinct roots. (a) Find the set of possible values for ( k ). (b) Consider the case when ( k=3 ). The roots of the equation can be expressed in the form ( p pm fracqsqrt3 ), where ( p, q in mathbbZ ). Find the value of ( p ) and of ( q ).$

Added by Maxi C.

IIT-JEE Super Course in Mathematics

Trishna Knowledge Systems 1st Edition

Chapter 2

Instant Answer

Solved by Expert Danielle Fairburn

11/30/2023

Step 1

The discriminant is given by $b^2 - 4ac$, where $a$, $b$, and $c$ are the coefficients of $x^2$, $x$, and the constant term, respectively. In this case, $a = k$, $b = 4k$, and $c = -1 - k$. So, we have: $(4k)^2 - 4(k)(-1 - k) > 0$ \(16k^2 - Show more…

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