Question

if the sum and product of the roots of the quadratic equation ax^—5x+ c=0 are each equal to 10 then the values of a and care​

Answer 1

Step-by-step explanation:

$\blue{\mathfrak{\underline{\large{Given}}}:} \\ \alpha + \beta = 10 \\ \alpha \beta = 10 \\ \blue{\mathfrak{\underline{\large{To \:find }}}:}value \:of \: a \: and \: c \\ \blue{\mathfrak{\underline{\large{Finding}}}:}\\ a {x}^{2} - 5x + c = 0 \\ \blue{\mathfrak{⟨\underline{\large{sum \: of \: zeros}}}⟩} \\ \alpha + \beta = \frac{ - b}{a} \\ 10 = \frac{ - ( - 5)}{a} \\ a = \frac{5}{10} \\ a= \frac{1}{2} \\ \blue{\mathfrak{⟨\underline{\large{Product \: of \: zeros}}}⟩} \\ \alpha \beta = \frac{c}{a} \\ 10 = \frac{c}{ \frac{1}{2} } \\ c = \frac{1}{2} \times 10 \\ c = 5$

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