Question

If Alpha and beta are the zeros of the quadratic polynomial FX equal to X square + bx + c then evaluate question Alpha minus beta. Solve the equation

Answer 1

Answer:

√(b² - 4ac) / a

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros.

★ The general form of a quadratic polynomial is ax² + bx + c .

★ If α and ß are the zeros of the given quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution:

Here,

The given quadratic polynomial is ;

f(x) = ax² + bx + c

Also,

It is given that , α and ß are the zeros of the quadratic polynomial f(x) .

Thus,

The sum of zeros of f(x) will be ;

α + ß = -b/a

Also,

The product of zeros of f(x) will be ;

αß = c/a

Now,

=> (α - ß)² = (α + ß)² - 4αß

=> (α - ß)² = (-b/a)² - 4c/a

=> (α - ß)² = b²/a² - 4c/a

=> (α - ß)² = (b² - 4ac)/a²

=> α - ß = √[(b² - 4ac)/a²]

=> α - ß = √(b² - 4ac) / a

Hence,

Required answer is : √(b² - 4ac) / a