Answer
Verified
396.6k+ views
Hint: We will first split the middle as to get -24 as the product of those two split terms. Then we will get factors and equate them to 0 to get the desired answer.
Complete step-by-step answer:
We will first know how to use the method of factorization.
Consider that we have an equation $a{x^2} + bx + c = 0$ ……….(1)
Then multiply a and c, we will get: ac
Now, we will find factors of ac such that the linear sum of those factors results in b.
Now, let us try to apply this method on ${x^2} + 5x - 24 = 0$.
Comparing this equation with equation (1), we will see that:-
a = 1, b = 5 and c = -24.
$a \times c = 1 \times ( - 24) = - 24$
Now, let us find all the factors of -24.
Factors = -1 and 24, -2 and 12, -3 and 8, -4 and 6, -6 and 4, -8 and 3, -12 and 2; and -24 and 1.
We see that -3 + 8 = 5.
We can rewrite our polynomial ${x^2} + 5x - 24 = 0$ as ${x^2} - 3x + 8x - 24 = 0$.
Now, taking $x$ common from first two terms and 8 common from the next two terms, we will have:-
$x(x - 3) + 8(x - 3) = 0$
Now, taking $x - 3$ common, we will have:-
$(x - 3)(x + 8) = 0$
We know that if a.b = 0, then either a = 0 or b = 0.
So, either $x - 3 = 0$ or $x + 8 = 0$.
Taking the constants on the right hand side in both equations:-
So, either $x = 3$ or $x = - 8$.
Hence, the roots are 3 and -8.
So, the correct answer is “Option D”.
Note: The student might make the mistake of finding a factor without considering the negative sign and will end up not getting any common factor among it.
There is one more way of doing the same question by using direct formula which says the roots of the equation $a{x^2} + bx + c = 0$ are given by $\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$.
Complete step-by-step answer:
We will first know how to use the method of factorization.
Consider that we have an equation $a{x^2} + bx + c = 0$ ……….(1)
Then multiply a and c, we will get: ac
Now, we will find factors of ac such that the linear sum of those factors results in b.
Now, let us try to apply this method on ${x^2} + 5x - 24 = 0$.
Comparing this equation with equation (1), we will see that:-
a = 1, b = 5 and c = -24.
$a \times c = 1 \times ( - 24) = - 24$
Now, let us find all the factors of -24.
Factors = -1 and 24, -2 and 12, -3 and 8, -4 and 6, -6 and 4, -8 and 3, -12 and 2; and -24 and 1.
We see that -3 + 8 = 5.
We can rewrite our polynomial ${x^2} + 5x - 24 = 0$ as ${x^2} - 3x + 8x - 24 = 0$.
Now, taking $x$ common from first two terms and 8 common from the next two terms, we will have:-
$x(x - 3) + 8(x - 3) = 0$
Now, taking $x - 3$ common, we will have:-
$(x - 3)(x + 8) = 0$
We know that if a.b = 0, then either a = 0 or b = 0.
So, either $x - 3 = 0$ or $x + 8 = 0$.
Taking the constants on the right hand side in both equations:-
So, either $x = 3$ or $x = - 8$.
Hence, the roots are 3 and -8.
So, the correct answer is “Option D”.
Note: The student might make the mistake of finding a factor without considering the negative sign and will end up not getting any common factor among it.
There is one more way of doing the same question by using direct formula which says the roots of the equation $a{x^2} + bx + c = 0$ are given by $\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE