Question

. If 5x^2− 6x + 5 = 0, then x +

1/x

equals

(a) −6
(b) 6
(c) −6/5
(d) 6/5





​

Answer 1

Step-by-step explanation:

Step by step solution :

STEP

1

:

Equation at the end of step 1

(5x2 + 6x) - 5 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 5x2+6x-5

The first term is, 5x2 its coefficient is 5 .

The middle term is, +6x its coefficient is 6 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 5 • -5 = -25

Step-2 : Find two factors of -25 whose sum equals the coefficient of the middle term, which is 6 .

-25 + 1 = -24

-5 + 5 = 0

-1 + 25 = 24

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

5x2 + 6x - 5 = 0

Answer 2

Answer:

The given equation is 5x

2

−6x+1=0 ........... (i)

General form of quadratic equation is given by ax

2

+bx+c=0 ....... (ii)

Comparing equation (i) with (ii) we have,

a=5,b=−6,c=1

The discriminant D is given by

D=b

2

−4ac=(−6)

2

−4(5)(1)=36−20=16

∴ Discriminant value is D=16

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