Question

write the sum and the product of the roots of
$2x {}^{2} + 10x - 5 = 0$


​

Answer 1

Sum of roots = -5
Product of roots = -5/2

Answer 2

❏ Used ForMuLaS:-

If $\alpha \:and \:\beta$ are two zeroes of the quadratic equation

➔ ax²+bf+c=0

And,the equation holding the sum and the product of the zeroes is given by,

➔$\bf \sf\boxed{x{}^{2}-(\alpha+\beta)x+\alpha \beta=0}$

❏ Question:-

Q) write the sum and the product of the roots of

$2x {}^{2} + 10x - 5 = 0$

❏ Solution:-

❚➾

Now,

$\sf\longrightarrow2x {}^{2} + 10x - 5 = 0$

$\sf\longrightarrow\frac{2x {}^{2} + 10x - 5}{2} = \frac{0}{2}$

$\sf\longrightarrow\frac{2x {}^{2}}{2} + \frac{10x}{2} - \frac{5}{2}= \frac{0}{2}$

$\sf\longrightarrow\frac{\cancel2x {}^{2}}{\cancel2} + \frac{\cancel{10}x}{\cancel2} - \frac{5}{2}= \frac{0}{2}$

$\sf\longrightarrow \boxed{x {}^{2}+ 5x - \frac{5}{2}= 0}.........(i)$

Now, comparing the equation (i) with the equation, x²-($\alpha+\beta$)x+$\alpha \beta$=0,

we get,

➝ ($\sf\bf \alpha+\beta$)= -5

And,

➝ ($\sf\bf \alpha\beta$)=($\bf\sf\frac{-5}{2}$)

∴ Sum of zeroes= -5

∴ Product if zeroes= $\sf\bf\frac{-5}{2}$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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