What is the value of (s+t) if the equation (3x2 + tx + s) has 2 and

Question

What is the value of (s+t) if the equation (3x^2 + tx + s) has 2 and 3 as its roots?

A. 2
B. 3
C. 7
D. 18
E. 33

Rabab36 · Answer

putting 2 and 3

we get 2 equations
12+2t=-12
3t+s=-27

solving we get s=18 t=-15

s+t=3

option B

bb · Answer

There is a trick for quadratic equation roots and their relationship for b and c For a quadratic  ax^2 + bx + c = 0  with roots R1 and R2:

Sum of roots : R1 + R2 = -b/c 
  Product of roots : R1 * R2 = c/a

Sum:  we get: 2 + 3 = - \frac{t}{3 }  and that translates into 5= - t/3 or t = -15

Product:  2 * 3 =  \frac{s}{3}  or 6 = s/3 or s=18

Thus s + t = (-15) + 18 = 3.

chetan2u · Answer

There are two ways to do it.
But prior to that, you should know what does 'roots of a quadratic equation' means.
Roots are the values of x that when substituted in equation will make the equation zero. A quadratic equation will have maximum two roots.

For example .. ax^2+bx+c=0  when x is replaced with the roots.

(1) Substitute the value of roots in equation
 3x^2 + tx + s 
Root 2:  3x^2 + tx + s ....  3*2^2 + t*2 + s=0......12+2t+s=0 ...(i)
Root 3:  3x^2 + tx + s ....  3*3^2 + t*3 + s=0......27+3t+s=0 ..(ii)
Subtract (i) from (ii)...15+t=0...t=-15
Now 12+2*(-15)+s=0...s=18
Thus s+t=18-15=3

(2) formula of sum and product
As also shown by  bb 
Sum of roots of a quadratic equation =  -\frac{b}{a} 
So 2+3=  -\frac{t}{3}  or t=5*(-3)=-15
Product of roots of a quadratic equation =  \frac{c}{a} 
So 2*3=  \frac{s}{3}  or s=6*3=18

Thus s+t = 18+(-15) = 3

ManishaPrepMinds · Answer

One more approach to solve such questions:

When roots (r1, r2) are given, rebuild the quadratic:
(x - r1)(x - r2) and then match coefficients.

Roots are 2 and 3 → factorized form of the equation:
(x - 2)(x - 3) = x^2 - 5x + 6 = 0 ...(1)

But our given equation is:
3x^2 + t x + s = 0 ...(2)
This is just equation (1) multiplied by 3.

Hence, multiplying equation (1) by 3:
3x^2 - 15x + 18 = 0

Comparing coefficients of equations (2) and the above:
t = -15, s = 18

Therefore:
s + t = 18 - 15 = 3

Answer: B (3)

Hope it’s clear!

What is the value of (s+t) if the equation (3x2 + tx + s) has 2 and

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What is the value of (s+t) if the equation (3x2 + tx + s) has 2 and

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