Question

find the value of k for which the equation 2x2-5x-k=0 is equal to

Answer 1

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ = > \bold \blue{2{x}^{2} - 5x - k = 0} \\ \\ \bold\red{\: compare \: the \: given \: equation \:} \\ \bold\red{with \: \: \: \purple{ a {x}^{2} + bx + c }} \\ \\ \bold\blue{hence \: \: \: \: a = 2 \: \: \: \: \: b = - 5 \: \: \: \: c = \:- k} \\ \\ \bold\purple{we \: use\:discriminate \: formula } \\ \\ = > \bold\red{ {b}^{2} - 4ac = 0 } \\ \\ = > \bold\red{{( - 5)}^{2} - 4(2)(-k) = 0} \\ \\ = > \bold\red{25+8(k) = 0} \\ \\ = > \bold\red{8(k) = - 25} \\ \\ = >\bold\red{ k= -\frac{25}{8} } \\ \\ \fbox \bold\purple{ \: i \: hope \: it \: helps \: you.}$

Answer 2

Solution :

Given :-

$\implies \sf 2{x}^{2} - 5x - k = 0$

On comparing with $\sf a{x}^{2}+ bx +c = 0$

We get

$\bullet \: \sf a = 2 \: \: \: \: \: \: \: \: \:\bullet \: b = - 5 \: \: \: \: \: \: \: \:\bullet \: c =-k$

By using discriminate formula

$\large\implies \underline{ \orange{ \sf{b}^{2} - 4ac = 0} }\\ \\ \implies \sf\ {( - 5)}^{2} - 4 \times 2 \times ( -k) = 0 \\ \\\implies \sf 25 + 8k = 0 \\ \\\implies \sf 8k = 25 \\ \\ \implies\underline{\boxed{ \sf \green{ k = - \frac{25}{8}}}}$