Question

Find the zeros of the polynomial 4x^+5√2x-3 and verify the relationship between the zeros and the coefficient of the polynomial urgent

Answer 1

Step-by-step explanation:

$4 {x}^{2} + 5 \sqrt{2}x - 3 = 0 = > 4 {x}^{2} + 6 \sqrt{2}x$

$- \sqrt{2}x - 3 = 0 = > 2 \sqrt{2}x( \sqrt{2}x + 3) -$

$1( \sqrt{2}x + 3) = 0 = > (2 \sqrt{2}x - 1)( \sqrt{2}x + 3) = 0$

so x = 1/2√2 or -3/√2. if the roots of the equation are a and b then the polynomial which has roots a and b are

${x}^{2} - (a + b)x + ab = 0$

in this case a+b =>1/2√2 -3/√2 =>(1-6)/2√2 =>5/2√2 and ab => (1/2√2)(-3/√2) => -3/4. So the polynomial which has roots 1/2√2 and -3/√2 is

${x}^{2} - ( \frac{ - 5}{2 \sqrt{2} })x - \frac{3}{4} = 0 = >$

Multiply on both sides by 4 then we get

$4 {x}^{2} + \frac{5}{2 \sqrt{2}} \times 4x - 3 = 0 = >$

$4 {x}^{2} + 5 \sqrt{2}x - 3 = 0$

Hence proved. Hope it helps you.