Question

find the zero of 4√3x²+5x-2√3 and verify relationship between the zero of cofficiens​

Answer 1

Step-by-step explanation:

$4 \sqrt{3} {x}^{2} + 5x - 2 \sqrt{3} = 0 \\ = > 4 \sqrt{3} {x}^{2} + 8x - 3x - 2 \sqrt{3} = 0 \\ = > 4x( \sqrt{3} x + 2) - \sqrt{3} ( \sqrt{3} x + 2) = 0 \\ = > (4x - \sqrt{3} )( \sqrt{3} x + 2) = 0 \\ = > 4x - \sqrt{3} = 0 \: \: | \sqrt{3} x + 2 = 0 \\ = > x = \frac{ \sqrt{3} }{4} \: \: \: | \: \: x = \frac{ - 2}{ \sqrt{3} } \\ \alpha = \frac{ \sqrt{3} }{4} \\ \beta = \frac{ - 2}{ \sqrt{3} }$

Now we know that

$a {x}^{2} + bx + c = 0 \: is \: the \:quadratic \: equation \: \\ whose \: zeros \: are \: \: \: \alpha \: \: and \: \: \beta \\ \alpha + \beta = \frac{ - b}{a} \\ \\ \alpha \beta = \frac{c}{a} \\ \alpha + \beta = \frac{5}{4 \sqrt{3} } \\ \\ \alpha \beta = \frac{ - 2 \sqrt{3} }{4 \sqrt{3} } \\ = \frac{ - 1}{2}$

Answer 2

ANSWER: Zeros are :  GIVEN:  TO VERIFY: Relationship between the zeros of the coefficients. SOLUTION Firstly we have to find the zeros of the given quadratic polynomial.  Verification: sum of zeros :  product of zeros  ADDITIONAL INFORMATION  where. a = coefficient of x^2.     b= coefficient of x c= constant term