Question

if alpha and beta are the roots of the equation 4x^2+3x +7=0 , then the value 1/alpha + 1/beta is

Answer 1

GIVEN:

• Quadratic equation : 4x² + 3x + 7 = 0
• α & β are the roots

TO FIND:

• 1/α + 1/β = ?

SOLUTION:

Here,

• Coefficient of x = 3
• coefficient of x² = 4
• constant term = 7

1/α + 1/β = -coefficent of x/constant term

1/α + 1/β = -3/7

Hence , 1/α + 1/β = -3/7

Derivation of formula (1/α + 1/β):-

We know that

• α + β = -coefficent of x/coefficient of x²
• αβ = constant/coefficient of x²

1/α + 1/β = α + β/αβ

1/α + 1/β = -coefficient of x/coefficient of x²/constant/coefficient of x²

→ 1/α + 1/β = -coefficent of x/constant

Answer 2

Answer:

1/α + 1/ß = – 3/7

Note:

★ The possible values of the variable which satisfy any equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ If α and ß are the two roots of the quadratic equation ax² + bx + c = 0 , then

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

Solution:

• Given : α and ß are the roots of the quadratic eqⁿ ; 4x² + 3x + 7 = 0
• To find : 1/α + 1/ß = ?

Here,

The given quadratic equation is ;

4x² + 3x + 7 = 0 .

On comparing with the general form of a quadratic equation ax² + bx + c = 0 ,

We have ;

a = 4

b = 3

c = 7

Also,

It is given that , α and ß are the roots of the given quadratic equation .

Thus,

=> Sum of roots = -b/a

=> α + ß = -3/4 ---------(1)

Also,

=> Product of roots = c/a

=> αß = 7/4 ---------(2)

Now,

1/α + 1/ß = (ß + α) / αß

= (α + ß) / αß

= (-3/4) / (7/4) { using eq-(1) , (2) }

= (-3/4) × (4/7)

= -3/7

Hence,

1/α + 1/ß = – 3/7