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What is the formula to solve the general form of quadratic equation and what is its discriminant value?

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Last updated date: 25th Jul 2024
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Answer
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Hint: In this problem, we can see the formula to solve the general form of the quadratic equation and what its discriminant value is. We should know that the general quadratic equation is of the form \[a{{x}^{2}}+bx+c=0\], where a, b, c are constant terms and a is not equal to zero. here we can see the formula which is used to solve the quadratic equation and its discriminant values.

Complete step by step answer:
Here we can see the formula to solve the general form of the quadratic equation and what its discriminant value is.
We should know that the general quadratic equation is of the form,
\[a{{x}^{2}}+bx+c=0\]
We can solve this type of quadratic equation using the quadratic formula,
\[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
We can also write it as,
\[x=\dfrac{-b\pm \sqrt{D}}{2a}\]
Where, the discriminant is denoted as \[\Delta \],
\[\Delta ={{b}^{2}}-4ac\]
We should know that,
If the discriminant value is equal 0, \[\Delta =0\]
Then we will have two real and equal roots (i.e. one real root).
If the discriminant value is greater than 0, \[\Delta >0\]
Then we will have two real and unequal roots.
If the discriminant value is less than 0, \[\Delta <0\]
Then we will have no real roots (imaginary roots).
 Therefore, the formula to solve a general quadratic equation \[a{{x}^{2}}+bx+c=0\] is \[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\], where the discriminant is \[\Delta ={{b}^{2}}-4ac\].

Note: We should always remember the condition of the discriminants which tells the type of roots, when the discriminant is equal to zero, the equation has one real root, when the discriminant is less than 0, it has no real roots and when the discriminant is greater than 0, then it has two real roots.