Question

solve the equation by using quadratic formula 1. √2x^2 +7x+5√2​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• √2x²+7x+5√2

${\sf{\green{\underline{\large{To\:find}}}}}$

• Zeroes by
• Quadratic formula

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Polynomial

• √2x²+7x+5√2

Here

From ax²+bx+c

• a=√2
• b=7
• c=5√2

Quadratic formula

$\tt{X=\dfrac{-b\pm{\sqrt{b^2-4ac}}}{2a}}$

¶utting the values

$\tt{X=\dfrac{-b\pm{\sqrt{b^2-4ac}}}{2a}}$

$\rightarrow\tt{X=\dfrac{-7\pm{\sqrt{49-40}}}{2\sqrt{2}}}$

$\rightarrow\tt{X=\dfrac{-7\pm{\sqrt{9}}}{2\sqrt{2}}}$

Taking x as +

$\rightarrow\tt{X=\dfrac{-7+{\sqrt{9}}}{2\sqrt{2}}}$

$\rightarrow\tt{X=\dfrac{-7+{3}}{2\sqrt{2}}}$

$\rightarrow\tt{X=\dfrac{-4}{2\sqrt{2}}}$

Taking x as -

$\rightarrow\tt{X=\dfrac{-7-{\sqrt{9}}}{2\sqrt{2}}}$

$\rightarrow\tt{X=\dfrac{-7-{3}}{2\sqrt{2}}}$

$\rightarrow\tt{X=\dfrac{-10}{2\sqrt{2}}}$

Additional Information

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

$\rightarrow\tt\alpha{+}\beta{=}\frac{-b}{a}$

&

$\rightarrow\tt\alpha{\times}\beta{=}\frac{c}{a}$

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-7}{\sqrt{2}}$

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:X}{Cofficient\:of\:x^2}=$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{5\sqrt{2}}{\sqrt{2}}$

$\rightarrow\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:x^2}}$

Hence,relation verified

Answer 2

S O L U T I O N :

$\bf{\large{\underline{\bf{Given\::}}}}$

√2x² + 7x + 5√2

$\bf{\large{\underline{\bf{To\:find\::}}}}$

The zeroes.

$\bf{\large{\underline{\bf{Explanation\::}}}}$

We know that formula of the quadratic equation :

$\boxed{\bf{x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} }}}}$

As we know that given polynomial compared with ax² + bx + c;

• a = √2
• b = 7
• c = 5√2

A/q

$\longrightarrow\sf{x=\dfrac{-7\pm\sqrt{(7)^{2}-4\times \sqrt{2}\times 5\sqrt{2} } }{2\sqrt{2} } }\\\\\\\longrightarrow\sf{x=\dfrac{-7\pm\sqrt{49-20\times 2} }{2\sqrt{2} } }\\\\\\\longrightarrow\sf{x=\dfrac{-7\pm\sqrt{49-40} }{2\sqrt{2} } }\\\\\\\longrightarrow\sf{x=\dfrac{-7\pm\sqrt{9} }{2\sqrt{2} } }\\\\\\\longrightarrow\sf{x=\dfrac{-7\pm3}{2\sqrt{2} } }\\\\\\\longrightarrow\sf{x=\dfrac{-7+3}{2\sqrt{2} } \:\;Or\:\:x=\dfrac{-7-3}{2\sqrt{2} } }$

$\longrightarrow\sf{x=\dfrac{-4}{2\sqrt{2} } \:\:\:Or\:\:\:x=\dfrac{-10}{2\sqrt{2} }}$