(B) For the quadratic equation $ax^{2}+bx+c=0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$.Comparing $x^{2}+5x+3=0$ with the sta

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$\frac{-5+\sqrt{13}}{2}, \frac{-5-\sqrt{13}}{2}$

(B) For the quadratic equation $ax^{2}+bx+c=0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$.Comparing $x^{2}+5x+3=0$ with the standard form,we get $a=1, b=5, c=3$.The discriminant $D = b^{2}-4ac = (5)^{2} - 4(1)(3) = 25 - 12 = 13$.Since $D > 0$,real solutions exist.Substituting the values into the formula: $x = \frac{-5 \pm \sqrt{13}}{2(1)}$.Thus,the solutions are $x = \frac{-5+\sqrt{13}}{2}$ and $x = \frac{-5-\sqrt{13}}{2}$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

Difficult

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+5x+3=0$.

A
$\frac{-5\sqrt{2}+\sqrt{74}}{6}, \frac{-5\sqrt{2}-\sqrt{74}}{6}$
B
$\frac{-5+\sqrt{13}}{2}, \frac{-5-\sqrt{13}}{2}$
C
$\frac{3+\sqrt{5}}{2}, \frac{3-\sqrt{5}}{2}$
D
$\frac{3+\sqrt{3}}{3}, \frac{3-\sqrt{3}}{3}$

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Mix Examples - Quadratic Equations

The perimeter of a bigger square is $12\,m$ more than the perimeter of a smaller square. Three times the area of the smaller square is $11\,m^2$ more than the area of the bigger square. Find the length of the side of the bigger square.

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Solve the following equation using the method of factorization: $x - \frac{20}{x} = 1$

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The necessary condition for $ax^2 + bx + c = 0$,where $a, b, c \in R$,to be a quadratic equation is:

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The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

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The speed of a motor-boat in still water is $x \, km/hr$ and the speed of the current of the river is $5 \, km/hr$. Given $x$ > 5, what is the time taken to cover a distance of $y \, km$ upstream?

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Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+5x+3=0$.

Similar Questions

The perimeter of a bigger square is $12\,m$ more than the perimeter of a smaller square. Three times the area of the smaller square is $11\,m^2$ more than the area of the bigger square. Find the length of the side of the bigger square.

Solve the following equation using the method of factorization: $x - \frac{20}{x} = 1$

The necessary condition for $ax^2 + bx + c = 0$,where $a, b, c \in R$,to be a quadratic equation is:

The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

The speed of a motor-boat in still water is $x \, km/hr$ and the speed of the current of the river is $5 \, km/hr$. Given $x$ > 5, what is the time taken to cover a distance of $y \, km$ upstream?

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