If one of the roots of 2x^{2} + 5x + 3 = 0 is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For a quadratic equation $ax^{2} + bx + c = 0$,the product of the roots is given by $\alpha \cdot \beta = c/a$.Given the equation $2x^{2} + 5x + 3

Vedclass · Accepted Answer

$-3/2$

Vedclass · Answer

(D) For a quadratic equation $ax^{2} + bx + c = 0$,the product of the roots is given by $\alpha \cdot \beta = c/a$.Given the equation $2x^{2} + 5x + 3 = 0$,we have $a = 2$,$b = 5$,and $c = 3$.Let the roots be $\alpha = -1$ and $\beta$ be the other root.Using the product of roots formula: $(-1) \cdot \beta = 3/2$.Therefore,$\beta = -3/2$.Alternatively,using the sum of roots: $\alpha + \beta = -b/a$.$-1 + \beta = -5/2$.$\beta = -5/2 + 1 = -3/2$.

If one of the roots of $2x^{2} + 5x + 3 = 0$ is $-1$,the other root is .............

Similar Questions

If $b=0$ and $c < 0$,is it true that the roots of $x^{2}+bx+c=0$ are numerically equal and opposite in sign? Justify.

Examine whether the following equation is quadratic or not: $3x^{2} + 5\sqrt{x} + 3 = 0$.

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

If one of the roots of the equation $x^{2} - \sqrt{p}x + q = 0$ where $p, q \in R$ is $x = -\sqrt{p}$,then prove that $2p + q = 0$.

$A$ train,travelling at a uniform speed for $360\, km$,would have taken $48\, min$ less to travel the same distance,if its speed were $5\, km/h$ more. Find the original speed of the train (in $km/h$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module