Answer :
The solution is Option A.
The value of the equation is x = -13/15 and x = 0
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
15x² + 13x = 0 be equation (1)
On simplifying the equation , we get
Subtracting 13x on both sides of the equation , we get
15x² = -13x
Divide by x on both sides of the equation , we get
15x = -13
Divide by 15 on both sides of the equation , we get
x = - ( 13/15 )
So , when x = 0
0 = 0
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = -13 ± √ ( 169 - 4 ( 15 ) ( 0 ) ) / 2 ( 15 )
x = -13 ± √ ( 169 - 0 ) / 30
x = ( -13 ± 13 ) / 30
So , we have 2 solutions to x ,
x = ( -13 - 13 ) / 30
x = -26 / 30
x = -13/15
And , x = ( -13 + 13 ) / 30
x = 0/30
x = 0
Hence , the solutions to the equation is x = -( 13/15 ) and x = 0
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The quadratic equation 15x^2 + 13x = 0 is solved using the quadratic formula, resulting in two solutions: x = 0 and x = -13/15.
To solve the quadratic equation 15x2 + 13x = 0, we can apply the quadratic formula. The quadratic formula states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found as:
x = - b ± √( b^2 - 4ac) / (2a)
Identifying the coefficients, we get a = 15, b = 13, and c = 0. Plugging these into the formula, we find:
x = - 13 ± √( 169 - 4 * 15 * 0) / (2 * 15)
Simplifying further, since the term under the square root is simply 169, we get:
x = - 13 ± √( 169) / (30)
Since the discriminant (the part under the square root) is positive and does not involve any subtraction due to c being zero, there is no need for plus or minus. We simply get two real solutions:
x = 0 (since anything times zero is zero)
x = - 13/30 (after taking negative of b over 2a)
Therefore, the solutions are x = 0 and x = -13/15.
