Question

√3x2 +5x- 8√3 middle term splitting

Answer 1

Answer:

x = -8/√3 , √3

Note:

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

★ To find the zeros of the polynomial p(x) , operate on p(x) = 0 .

★ A quadratic polynomial can have atmost two zeros .

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

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of any quadratic polynomial , then it is given by ;

x² - (α + ß)x + αß

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then they (α and ß) are also the zeros of the quadratic polynomial k(ax² + bx + c) , k≠0.

Solution:

Here,

The given quadratic polynomial is ;

√3x² + 5x - 8√3

We need to find the zeros of the given quadratic polynomial using middle term splitting method.

To find the zeros of the given quadratic polynomial , let's equate it to zero .

Thus,

=> √3x² + 5x - 8√3 = 0

=> √3x² + 8x - 3x - 8√3 = 0

=> x(√3x + 8) - √3(√3x + 8) = 0

=> (√3x + 8)(x - √3) = 0

=> x = -8/√3 , √3

Hence,

The required answer is :

x = -8/√3 , √3