1 Answer

CrepeGoat · Answer 1 · 2023-12-20T05:31:56+0000

So, we need to solve the quadratic equation from quadratic formula as per the question, but before starting, let's first recall that, for any quadratic equation of the form ax² + bc + c = 0, the discriminant is given by D = b² - 4ac, and the value of x is given by :

${\boxed{\bf{x=(-b\pm √(D))/(2a)}}}$

Also, their are no real solutions of x i.e their are only imaginary values of x iff D < 0, equal and real roots iff D = 0 and real and distinct roots iff D > 0. So, let's convert the given equation to the standard form ax² + bx + c = 0 and then we will find the discriminant and then we will be solving for k ;

${:\implies \quad \sf 2k(k+5)=-25}$

${:\implies \quad \sf 2k^(2)+10k=-25}$

${:\implies \quad \sf 2k^(2)+10k+25=0}$

Now, on comparing this with the standard equation, we will get a = 2, b = 10 and c = 25, and then D = (10)² - 4 × 2 × 25 = 100 - 200 = - 100, now as D < 0, so their will be imaginary values of k, so now solving for k will yield by using the Quadratic Formula ;

${:\implies \quad \sf k=(-10\pm √(-100))/(2* 2)}$