Question

For what values of a and b, x= 3/4 and x = — 2 are solutions of the equation ax2 + bx — 6 = 0.

Answer 1

Question:

For what value of a and b ,x = ,3/4 and x = -2 are solutions of the equation ax² + bx - 6 = 0.

Answer:

a = 4 , b = 5

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Solution:

The given quadratic equation is :

ax² + bx - 6 = 0.

Also,

It is given that , x = 3/4 and x = -2 are the roots of the given equation, thus they must satisfy the equation.

Thus,

=> a(3/4)² + b(3/4) - 6 = 0

=> 9a/16 + 3b/4 - 6 = 0

=> 3(3a/16 + b/4 - 2) = 0

=> 3a/16 + b/4 - 2 = 0

=> (3a + 4b - 32)/16 = 0

=> 3a + 4b - 32 = 0 --------(1)

Also,

=> a(-2)² + b(-2) - 6 = 0

=> 4a - 2b - 6 = 0

=> 2•(4a - 2b - 6) = 2•0

=> 8a - 4b - 12 = 0 --------(2)

Adding eq-(1) and (2) , we get ;

=> 3a + 4b - 32 + 8a - 4b - 12 = 0

=> 11a - 44 = 0

=> 11a = 44

=> a = 44/11

=> a = 4

Now,

Putting a = 4 in eq-(1) , we have ;

=> 3a + 4b - 32 = 0

=> 3•4 + 4b - 32 = 0

=> 12 + 4b - 32 = 0

=> 4b - 20 = 0

=> 4b = 20

=> b = 20/4

=> b = 5

Hence,

The required values of a and b are 4 and 5 respectively.

Answer 2

Step-by-step explanation:

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