Question

If the difference between the roots of the equation x2-13x + k = 0 is 17 find k​

Answer 1

Answer:

The quadratic eq is x² - 13x + k = 0

and

The difference between the roots of quadratic equation is 17 i.e

\sf \Rightarrow α - β = 17 \: --- \: (i)⇒α−β=17−−−(i)

We know that , the sum of roots i.e α + β is

\sf \star \: \: \alpha + \beta = - \frac{b}{a}⋆α+β=−

a

b

Thus ,

\sf \Rightarrow α + β = 13 \: - - - \: (ii)⇒α+β=13−−−(ii)

Add eq (i) and (ii) , we get

\begin{gathered}\sf \Rightarrow 2α = 30 \\ \\ \sf \Rightarrow α = \frac{30}{2} \\ \\ \sf \Rightarrow α = 15\end{gathered}

⇒2α=30

⇒α=

2

30

⇒α=15

Put the value of α = 15 in eq (ii) , we get

\begin{gathered}\sf \Rightarrow 15 + β = 13 \\ \\ \sf \Rightarrow β = 13 - 15 \\ \\ \sf \Rightarrow β = -2\end{gathered}

⇒15+β=13

⇒β=13−15

⇒β=−2

Now , the product of roots i.e α × β is

\sf \star \: \: \alpha \times \beta = \frac{c}{a}⋆α×β=

a

c

Thus ,

\begin{gathered}\sf \Rightarrow 15 × -2 = k \\ \\ \sf \Rightarrow k = -30\end{gathered}

⇒15×−2=k

⇒k=−30

\therefore \underline{ \sf \bold{The \: value \: of \: k \: is -30}}∴

Thevalueofkis−30