Question

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: 4x²+5√2x-3​

Answer 1

${\huge{\fbox{\colorbox{black}{\color{hotpink}{\textbf{\textsf{Answer:-}}}}}}}$

${ \sf{4 {x}^{2} + 5 \sqrt{2} x - 3 = 0}}\\ \\{ \sf{ 4 {x}^{2} + 6 \sqrt{2} x - \sqrt{2} x - 3 = 0 }}\\ \\ { \sf{2 \sqrt{2} x( \sqrt{2} x + 3) - 1( \sqrt{2}x + 3) = 0 }} \\ \\ { \sf{( \sqrt{2}x + 3)(2 \sqrt{2}x - 1) = 0 }} \\ \\{ \sf{ \blue{ x = \frac{ - 3}{ \sqrt{2} } \: \: \: \: \: \: \: \: x = \frac{1}{2 \sqrt{2} } }}} \\ \\ \\ { \underline{ \sf{ \red{Verification : - }}}} \\ \\ { \sf{1) \: \: \alpha + \beta = \frac{ - b}{a} }} \\ \\ { \sf{\frac{ - b}{a} = \frac{ - 5 \sqrt{2} }{4}}} \\ \\ { \sf{ = > \frac{ - 3}{ \sqrt{2} } + \frac{1}{2 \sqrt{2} } = \frac{ - 6 \sqrt{2} + \sqrt{2} }{4} }} \\ \\ { \sf{ \frac{ - 5 \sqrt{2} }{4} }} \\ \\ { \sf{ \red{Hence \: \: Verified}}} \\ \\ { \sf{2) \alpha . \beta = \frac{c}{a} }} \\ \\ { \sf{\frac{c}{a} = \frac{ - 3}{4}}} \\ \\ { \sf{ \frac{ - 3 }{ \sqrt{2} } \times \frac{1}{2 \sqrt{2} } = \frac{ - 3}{4}}} \\ \\ { \sf{ \red{Hence \: \: Verified}}}$

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