Question

Find the roots of the equation:

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Answer 1

Step-by-step explanation:

Given -

• x + 1/x = 4¼

To Find -

• Roots of the equation

x + 1/x = 17/4

» x² + 1/x = 17/4

» x² + 1 = 17x/4

» x² + 17x/4 + 1 = 0

» 4x² + 17x + 4/4 = 0

» 4x² + 17x + 4 = 0

Now,

Factorising this equation, we get :

» 4x² + 16x + x + 4

» 4x(x + 4) + 1(x + 4)

» (4x + 1)(x + 4)

Zeroes are -

4x + 1 = 0 and x + 4 = 0

• x = -1/4 and x = -4

Verification :-

• α + β = -b/a

» -1/4 - 4 = -17/4

» -1 - 16/4 = -17/4

» -17/4 = -17/4

LHS = RHS

And

• αβ = c/a

» -1/4 × -4 = 4/4

» 1 = 1

LHS = RHS

Hence,

Verified..

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{the \: value \: of \: 4x² \: + \: 17x \: + \: 4 \: is \: x \: = \: (-1/4 \: , \: -4).}$

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

• x + 1/x = 4 ¹/4

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

• Equation of the roots.

$\large\underline\mathrm{Solution}$

$\implies$ x + 1/x = 17/4

$\implies$ (x² + 1)/x = 17/4

$\implies$ x² + 1 = 17x/4

$\implies$ x² + 17x/4 + 1 = 0

$\implies$ (4x² + 17x + 4)/4

$\implies$ 4x² + 17x + 4 = 0

$\large\underline\mathrm{Now}$

$\large\underline\mathrm{factorising \: in \: this \: equation.}$

$\implies$ 4x² + 17x + 4 = 0

$\implies$ 4x(x + 4) + 1(x + 4) = 0

$\implies$ (4x + 1)(x + 4)

$\implies$ 4x + 1 = 0

$\implies$ x = -1/4

$\implies$ x + 4 = 0

$\implies$ x = -4

$\large\underline\mathrm{hence}$

$\large\underline\mathrm{the \: value \: of \: 4x² \: + \: 17x \: + \: 4 \: is \: x \: = \: (-1/4 \: , \: -4).}$

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