Question

If the difference between the roots of the x square - 13 x + k is equal to zero is 17 find k

Answer 1

Step-by-step explanation:

Given -

• If the difference between the roots of the x² - 13x + k is equal to zero is 17

To Find -

• Value of k

As we know that :-

• α + β = -b/a

→ α + β = -(-13)/1

→ α + β = 13 ........ (i)

And

→ α - β = 17 (given) ....... (ii)

Now, From (i) and (ii), we get :

→ α + β = 13

α - β = 17

__________

→ 2α = 30

→ α = 30/2

→ α = 15

Now, Substituting the value of α on (i), we get :

→ α + β = 13

→ 15 + β = 13

→ β = -2

And

As we know that :-

• αβ = c/a

→ 15 × -2 = k/1

→ k = -30

Hence,

The value of k is -30

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\large\underline\mathrm{The \: value \: of \: k \: is \: -30}$

$\large\underline\mathrm{Given:-}$

• the difference between the roots of the x² - 13 x + k is equal to zero is 17.

$\large\underline\mathrm{To \: find}$

• value of k ?

$\large\underline\mathrm{Solution}$

$\implies$ α + β = -b/a

$\implies$ α + β = -(-13)/1

$\implies$ α + β = 13. ...(1)

$\large\underline\mathrm{and}$

$\implies$ α - β = 17. ...(2) ..(given)

$\large\underline\mathrm{now,}$

$\large\underline\mathrm{putting \: the \: Eq. \: (1) \: and \: (2)}$

$\implies$ α + β = 13

$\implies$ α - β = 17

$\implies$ 2α = 30

$\implies$ α = 30/2

$\implies$ α = 15

$\large\underline\mathrm{now,}$

$\large\underline\mathrm{putting \: the \: value \: of \: α \: in \: Eq. \: (1) \: .}$

$\implies$ α + β = 13

$\implies$ 15 + β = 13

$\implies$ β = 13 - 15

$\implies$ β = - 2

$\large\underline\mathrm{and}$

$\implies$ βα = c/a

$\implies$ 15 × -2 = k/1

$\implies$ -30 = k

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{The \: value \: of \: k \: is \: -30}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$