Mathematics

Grade10

Easy

Question

Find the solutions for the equation $x squared minus 10 x plus 12 equals 0$

$5 + \sqrt{13} and 5 - \sqrt{13}$
$- 5 + \sqrt{13} and 5 - \sqrt{13}$
$5 - \sqrt{13} and - 5 - \sqrt{13}$
$5 + \sqrt{13} and - 5 - \sqrt{13}$

hint Hint:

Prime factorization of any number can be done by using two methods: (1) Division method and (2) Factor tree method .

The correct answer is: $5 plus square root of 13 text and end text 5 minus square root of 13$

Given equation $x squared minus 10 x plus 12 equals 0$ ,
Rewrite the given equation in the form
We get,
$x squared minus 10 x plus 12 equals 0$
Add 25 on both the sides, as $open parentheses 10 over 2 close parentheses squared equals 25$ , we get
$x squared minus 10 x plus 25 equals negative 12 plus 25 x squared minus 10 x plus 25 equals 13 left parenthesis x minus 5 right parenthesis squared equals 13$
Take square root on both the sides, we get
$square root of left parenthesis x minus 5 right parenthesis squared end root equals plus-or-minus square root of 13 x minus 5 equals plus-or-minus square root of 13$
Add 5 on both the sides, we get
$x minus 5 plus 5 equals 5 plus-or-minus square root of 13 x equals 5 plus-or-minus square root of 13$
The solutions are $5 plus square root of 13$ and $5 minus square root of 13$

In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.

$x squared plus 8 x plus c$ .Find the value of ‘c’ that makes the expression a perfect square trinomial.

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The coordinates of the vertex of the parabola, whose equation is y = 2x² + 4x - 5 are:

The other method to find the vertex of a parabola is as We know that the x-coordinate of a vertex, (i.e) h is -b/2a. Now, substitute the x-coordinate value in the given standard form of the parabola equation y=ax2+bx+c, we will get the y-coordinate of a vertex.

The coordinates of the vertex of the parabola, whose equation is y = 2x² + 4x - 5 are:

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Find the solutions for the equation

Prime factorization of any number can be done by using two methods: (1) Division method and (2) Factor tree method .

The correct answer is:

Given equation ,Rewrite the given equation in the formWe get,Add 25 on both the sides, as , we getTake square root on both the sides, we getAdd 5 on both the sides, we getThe solutions are and

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Find the solutions for the equation $x squared minus 10 x plus 12 equals 0$

The correct answer is: $5 plus square root of 13 text and end text 5 minus square root of 13$

$x squared plus 8 x plus c$ .Find the value of ‘c’ that makes the expression a perfect square trinomial.

$x squared plus 8 x plus c$ .Find the value of ‘c’ that makes the expression a perfect square trinomial.

The coordinates of the vertex of the parabola, whose equation is y = 2x² + 4x - 5 are:

The coordinates of the vertex of the parabola, whose equation is y = 2x² + 4x - 5 are:

Find the solution of quadratic equation $8 x squared minus 10 equals 54$ using square roots.

Find the solution of quadratic equation $8 x squared minus 10 equals 54$ using square roots.

Find the solution of quadratic equation $6 x squared minus 13 equals 23$ using square roots.

Find the solution of quadratic equation $6 x squared minus 13 equals 23$ using square roots.

Find the solution of quadratic equation $x squared plus 1 equals 1$ using square roots.

Find the solution of quadratic equation $x squared plus 1 equals 1$ using square roots.

Determine the type of solution of the quadratic equation $x squared minus x plus 41 equals 0$ .

Determine the type of solution of the quadratic equation $x squared minus x plus 41 equals 0$ .

Find the discriminant of the quadratic equation $5 x squared minus 8 x plus 1 equals 0$ .

Find the discriminant of the quadratic equation $5 x squared minus 8 x plus 1 equals 0$ .

Draw the graph for the quadratic equation $x squared minus 2.5 x plus 1 equals 0$ . Give answers correct to 1 decimal place where appropriate.

Draw the graph for the quadratic equation $x squared minus 2.5 x plus 1 equals 0$ . Give answers correct to 1 decimal place where appropriate.

Find the solutions using graph for the quadratic equation $x squared minus 7 x plus 4 equals 0$ .

Find the solutions using graph for the quadratic equation $x squared minus 7 x plus 4 equals 0$ .

Find the type of solutions for the quadratic equation $x squared plus 12 x minus 45 equals 0$ .

Find the type of solutions for the quadratic equation $x squared plus 12 x minus 45 equals 0$ .

Find the discriminant of the quadratic equation $x squared minus 2 x plus 3 equals 0$ .

Find the discriminant of the quadratic equation $x squared minus 2 x plus 3 equals 0$ .