Question

The roots of 7x^2 + x - 5 = 0 are a and b Compute (a - 4)(b - 4).

Answer 1

Answer:

15 6/7

Step-by-step explanation:

The roots of 7x^2 + x - 5 = 0 are a and b.

Compute (a - 4)(b - 4).

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Use of this information:

• For the quadratic equation ax^2+bx+c=0, the sum of its roots = –b/a and the product of its roots = c/a.

In given case:

• sum of roots=a+b= - 1/7

• product of roots=ab= -5/7

Now let's find the value of (a-4)(b-4)

• (a-4)(b-4)=
• ab-4(a+b)+16=
• -5/7-4(-1/7)+16=
• -1/7+16=
• 15 6/7

Answer is 15 6/7