Question

How do you solve $ 4{x^2} + 17x + 15 = 0 $ ?

Answer 1

Hint: The equation given in the question is quadratic; a quadratic equation is a type of polynomial equation. An algebraic expression contains numerical values and alphabets representing the unknown variable quantities. When these unknown quantities are raised to some power such that the power is a non-negative integer and the numerical values are written as coefficients, the algebraic expression is called a polynomial.

Complete step-by-step answer:
For solving these equations, there are several methods like factorization, completing the square, quadratic formula, etc. Using the appropriate method, we can find out the correct answer.
The given equation is $ 4{x^2} + 17x + 15 = 0 $
It can be solved by factorization as well as –
 $
  4{x^2} + 12x + 5x + 15 = 0 \\
  4x(x + 3) + 5(x + 3) = 0 \\
   \Rightarrow (4x + 5)(x + 3) = 0 \\
   \Rightarrow x = - \dfrac{5}{4},\;x = 3 \;
  $
Hence, the factors of the equation are $ x + \dfrac{5}{4} = 0 $ and $ x - 3 = 0 $ .
So, the correct answer is “ $ x + \dfrac{5}{4} = 0 $ and $ x - 3 = 0 $ ”.

Note: The values of the unknown variable at which the function comes out to be zero are called the roots of the equation, they are simply the x-intercepts as the value of y is zero at x-axis. For finding the roots by factorization, we first convert the given equation in the standard equation form that is $ a{x^2} + bx + c = 0 $ and then comparing the given equation and the standard equation, we find the values of a, b and c. Then we write b as a sum of two numbers such that their product is equal to the product of a and c, that is, $ {b_1} \times {b_2} = a \times c $ . We find the value of $ {b_1} $ and $ {b_2} $ by hit and trial, if we are not able to solve an equation by factorization then we move to the quadratic formula.