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Quadratic Equations

Long Answer Type

371.

A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

Multiple Choice Questions

372.

If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0, then ab equals

3
$- \frac{7}{2}$
6
-3

Long Answer Type

373.
Find the values (s) of k so that the quadratic equation 3x² - 2kx + 12 = 0 has equal roots.

Given quadratic equation is 3x² - 2kx + 12 = 0

Here a = 3, b = -2k, c = 12

The quadratic equation will have equal roots if $∆$ = 0.

$∴$ b² - 4ac = 0

Putting the values of a, b and c we get

= ( -2k )² - 4 (3) (12) = 0

$\Rightarrow$ 4k ² - 144 = 0

$\Rightarrow$ 4k ² = 144

$\Rightarrow k^{2} = \frac{144}{4} \Rightarrow k = 36 Considering square root on both sides, k = \sqrt{36} = \pm 6$

Therefore, the required values of k are 6 and -6.

374.

Solve for x: 4x² – 4ax + (a² – b²) = 0

Solve for x: 3x² - $\sqrt{6}$ x + 2 = 0

375.

A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. Find the number of books he bought.

The sum of two number is 9 and the sum of their reciprocals is $\frac{1}{2}$ . Find the numbers.

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

Multiple Choice Questions

Long Answer Type

373. Find the values (s) of k so that the quadratic equation 3x2 - 2kx + 12 = 0 has equal roots.

373.
Find the values (s) of k so that the quadratic equation 3x² - 2kx + 12 = 0 has equal roots.