find the value of 'k' and other root if the difference of roots of the eqn x2-kx+6=0 is 5 - Maths - Quadratic Equations

Question

find the value of 'k' and other root if the difference of roots
of the eqn x2-kx+6=0 is 5 ???

Gursheen kaur. · Accepted Answer

Let the first root of the equation be $α$ .and the second root of the equation be ( $α$ + 5).As, sum of roots $= - \frac{b}{a}$

Product of roots $= \frac{c}{a}$

Given: quadratic equation is: x²-kx+6=0

∴ $α$ + ( $α$ + 5) = k

⇒ 2 $α$ + 5 = k

⇒ 2 $α$ = k – 5

$\Rightarrow α = \frac{k - 5}{2} ........ (i)$

And, $α$ ( $α$ + 5) = 6

$\Rightarrow \frac{k - 5}{2} [(\frac{k - 5}{2}) + 5] = 6 [Putting the value of α] \Rightarrow \frac{k - 5}{2} [\frac{k - 5 + 10}{2}] = 6 \Rightarrow \frac{k - 5}{2} [\frac{k + 5}{2}] = 6 \Rightarrow \frac{(k - 5) (k + 5)}{4} = 6 \Rightarrow \frac{k^{2} - 25}{4} = 6 \Rightarrow k^{2} - 25 = 4 \times 6 \Rightarrow k^{2} = 24 + 25 = 49 \Rightarrow k = 7$

put the value of k in (i), we get,

$\Rightarrow α = \frac{7 - 5}{2} = \frac{2}{2} \Rightarrow α = 1$

∴ the first root is 1 and second root is 1+5=6

Thus, the value of k=7

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find the value of 'k' and other root if the difference of roots of the eqn. x2-kx+6=0 is 5 ???

find the value of 'k' and other root if the difference of roots of the eqn. x²-kx+6=0 is 5 ???