| Directions: Assertion-Reason type questions. Each of these questions contains two statements: Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the codes [a], [b], [c] and [d] in the given below: |
| Statement I : If equations \[a{{x}^{2}}+bx+c=0;\] \[(a,b,c\in R)\]and 2x2 + 3x + 4 = 0 have a common root, then a : b : c = 2 : 3 : 4. |
| Statement II: Roots of 2x2 + 3x + 4 = 0 are imaginary. |
A) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B) Statement I is true, Statement II is false.
C) Statement I is false. Statement II is true.
D) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
Correct Answer: A
Solution :
Given equation is 2x2 + 3x + 4 = 0 Now, discriminate = (3)2 - 4 . 2- 4 = - 23 < 0 Hence, roots of above equation are imaginary \[\therefore \]Statement II is true. Since, 2,3,4 e R, therefore roots are conjugate to each other. But it is given one root is common in ax2 + bx + c = 0 and 2x2 + 3x + 4 = 0. If one root is common, then other root is also common. \[\therefore \]Roots are conjugate (a, b, c e R). Hence, both equations are identical. a :b : c = 2 : 3 : 4 Hence, Statement I is true.
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