One root of the equation 3x2 - 10x + 3 = 0 is	1	. Find the other root.
	3

Correct Answer: ?11

Explanation:

The given quadratic equation 3x² + (k ? 1)x + 9 = 0
Putting x = 3 in above given eq. , we get
27 + 3(k ? 1) + 9 = 0
? 27 + 3k - 3 + 9 = 0
? 3k = ?33 ? k = ?11.
Hence , the value of k is ?11.

Correct Answer: p2 < 4q

Explanation:

According to question , we can say that
The equation x² ? px + q = 0, p, q ? R has no real root
On comparing with quadratic eq. Ax² + Bx + C = 0 , we get
? A =1, B= - p, C = q
Now ,we have B² < 4AC
? ( - P )² < 4 x 1 x q
? p² < 4q.
Hence , option B is correct answer .

Correct Answer: 1

Explanation:

Given that :- Given that :- ?. 5x + 2y = 31 .....( 1 )
?. 3x + 7y = 36 .....( 2 )
Solving these two linear equations, we get x = 5, y = 3 .
? x > y is correct answer .

Correct Answer: 4

Explanation:

As per the given above equations , we have
From equation ?. x² - 7x + 12 = 0
? x² - 4x - 3x + 12 = 0
? x( x - 4) - 3( x - 4) = 0
? ( x - 4) ( x - 3) = 0
? x = 4 or, 3
?. y² - 12y + 32 = 0
? y² - 8y - 4y + 32 = 0
? y( y - 8) - 4( y - 8) = 0
? ( y - 8) ( y - 4) = 0
? y = 4 or, 8
Thus , x ? y is required answer .

Correct Answer: 3

Explanation:

Correct Answer: (2 + x + 4) (2 ? x + 4)

Explanation:

The given expression x⁴ + 7x² + 16 = ( x⁴ + 8x² + 16 ) - x²
= ( x⁴ + 2 * 4 * x² + 4² ) - x²
= ( x² + 4 )² - x²
= ( x² + 4 + x ) ( x² + 4 - x )
Hence , x⁴ + 7x² + 16 = ( x² + x + 4 ) ( x² - x + 4 ).
Option C is correct answer .

Correct Answer: 2

Explanation:

As per the given above question , we can say that
The given quadratic equations are
x² - 7x + 10 = 0 ? (x ? 5)(x ? 2) = 0 ? x = 5, 2
And x² - 10x + 16 = 0 ? (x ? 8)(x ? 2) = 0 ? x = 8, 2
? Common root is 2.

Correct Answer: 10, 6

Explanation:

Let the smaller part be x. Then the larger part = 16 ? x.
According to question , we have
2( larger part )² - ( smaller part )² = 164
Now , 2( 16 - x )² - x² = 164
? 2( 256 + x² - 32x ) - x² = 164
? x² - 64x + 348 = 0
? x² - 6x - 58x + 348 = 0
? x(x - 6) - 58(x - 6) = 0
? (x - 6) (x - 58)
x = 6 or x = 58
But m = 58 is not possible, since sum of the two parts is 16
? smaller part ( x ) = 6,
? other part = 16 - x = 16 - 6 = 10.
Hence , required answer will be option A .

Correct Answer: 2, ?1

Explanation:

Given equation is
2x - x² = x - 2 ? x² - x - 2 = 0
? ( x + 1 ) ( x - 2 ) = 0
? x = 2 or = - 1.
Therefore , option B is correct answer .

Correct Answer: 11, ?5

Explanation:

Given that : - log₁₀ ( x² - 6x + 45 ) = 2
? x² - 6x + 45 = 10² = 100
? x² - 6x - 55 = 0
? ( x - 11 ) ( x + 5 ) = 0
? x = 11 or x = - 5.
Hence , the values of x are 11 and - 5.