The roots of the equation ax² + bx + c = 0 will be reciprocal if

Correct Answer: 28

Explanation:

Let, the two natural consecutive odd numbers be n and (n + 2)
Now, according to the question,
? n² + ( n + 2 )² = 394
? n² + n² + 4 + 4n = 394
? 2n² + 4n - 390= 0
? n² + 2n - 195 = 0
? n² + 15n - 13n - 195 = 0
? n( n + 15 ) - 13( n + 15 ) = 0
? ( n + 15 ) ( n - 13 ) = 0
? n = 13 and n ? - 15
? The two natural consecutive odd numbers be 13 and (13 + 2) = 15 .
? the sum of the numbers = 13 + 15 = 28
Quicker Approach:
By mental operation, 13² + 15² = 169 + 225 = 394
? Required sum = 13 + 15 = 28

Correct Answer: 6

Explanation:

According to question ,we can say that
Let , x = ?30 + ?30 + ?30 +........
On squaring both sides, we have
x² = 30 + ?30 + ?30 + ?30 +........
? x² = 30 + x ? x² - x - 30 = 0
? x² - 6x + 5x - 30 = 0
? x( x - 6 ) + 5( x - 6 ) = 0
? ( x - 6 ) ( x + 5 ) = 0
? x = 6 because x ? - 5
Hence , required answer is 6 .

Correct Answer: (a ? 2b ? 4) (a ? 2b + 2)

Explanation:

Given that :- The factors of a² + 4b² + 4b ? 4ab ? 2a ? 8
= a² + 4b² ? 4ab ? 2a + 4b ? 8
= (a ? 2b) ² ? 2(a ? 2b) ? 8
Let, (a ? 2b) = x
? The given expression = x² ? 2x ? 8
= x² ? 4x + 2x ? 8
= x(x ? 4) + 2(x ? 4)
= (x ? 4) (x + 2)
Putting the value of x , we get
? a² + 4b² + 4b ? 4ab ? 2a ? 8 = (a ? 2b ? 4) (a ? 2b + 2)
Therefore , required answer will be (a ? 2b ? 4) (a ? 2b + 2) .

Correct Answer: 2x2 - 5x + 2 = 0

Explanation:

Correct Answer: 11, 13

Explanation:

According to question ,
Let, the two consecutive odd positive integers be 2x + 1 and 2x + 3 where x is a whole number.
Now, ( 2x + 1 )² + ( 2x + 3 )² = 290
? 4x² + 4x + 1 + 4x² + 12x + 9 = 290
? 8x² + 16x - 280 = 0
? x² + 2x - 35 = 0
? ( x + 7 ) ( x - 5 ) = 0
? x = 7, - 5
But, x = ?7 is not possible, since ?7 is not a whole number .
? x = 5.
We get , 2x + 1 = 2 x 5 + 1 = 11 and 2x + 3 = 2 x 5 + 3 = 13
Thus , two consecutive positive odd integers are 11 and 13 .

Correct Answer: 1

Explanation:

According to question ,we have
From equation ?. x² ? 4 = 0
? x = ± 2,
From equation ?. y² + 6y + 9 = 0
? ( y + 3 )² = 0
? ( y + 3 )( y + 3 ) = 0
? y + 3 = 0 ? y = -3 , -3
Clearly , x > y is required answer .

Correct Answer: 4

Explanation:

According to question ,we have
From equation ?. x² = 729
? x = ± ?729 = ± 27
From equation ?. y = ?729
? y = 27
Hence , x ? y is required answer .

Correct Answer: 3

Explanation:

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: 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 .