Question

find the value of discriminat (∆)for the quadratic equation x²-6x-5=0.​

Answer 1

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

Quadratic equation :

• $\sf\:x^{2}-6x-5=0$

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

• Discriminant of the given quadratic equation

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$\large\sf\underline{Formula\:to\:be\:used\::}$

• Discriminant = $\small{\mathfrak\purple{b^{2}-4ac}}$

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$\large\sf\underline{Concept\::}$

In this question we are asked to find the discriminant for $\sf\:x^{2}-6x-5=0$. Doing so is simple by using the formula. But to use formula we must know the value of a, b and c. To get the value of a, b and c we would compare the given equation with the general form of the quadratic equation $\sf\:ax^{2}+bx+c$. This would help us to get the values of a, b and c, after which we can easily find the Discriminant using formula. Let's begin !

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$\large\sf\underline{Solution\::}$

We know quadratic equation is usually in the form $\sf\:ax^{2}+bx+c$.

So comparing $\sf\:x^{2}-6x-5=0$ with $\sf\:ax^{2}+bx+c$ we get :

• a = $\tt\pink{1}$

• b = $\tt\pink{(-6)}$

• c = $\tt\pink{(-5)}$

Now as we know the value for a , b and c let's use the formula :

$\sf\rightarrow\:Discriminant\:=\:b^{2}-4ac$

• Let's substitute the values of a, b and c

$\sf\rightarrow\:Discriminant\:=\:(-6)^{2}-4(1)(-5)$

$\sf\rightarrow\:Discriminant\:=\:36-4 \times 1 \times (-5)$

$\sf\rightarrow\:Discriminant\:=\:36-4 \times (-5)$

$\sf\rightarrow\:Discriminant\:=\:36-(-20)$

$\sf\rightarrow\:Discriminant\:=\:36+20$

$\small{\underline{\boxed{\mathrm\red{\rightarrow\:Discriminant\:=\:56}}}}$ ★

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!! Hope it helps !!