Question

Question 6
The values of a for which the expression x? -(a +2)x+ 4 is always positive is/are
(a) 2 <a<6
(b) -6<a<2
(c) -2 <a<6
(d) -6<a<-2
Question 7
If the difference between the roots of the equation r’ + ax+8 = 0 is 2, then the values of a
will be
(a) a= +8
(b) a = +6
(c) a = +7
(d) a = + 9​

Answer 1

Answer:

no idea about this this is my answer

Answer 2

Answer:

question number 6

answer is (b) -6 < a < 2

Step-by-step explanation:

for question number 6

• x² - (a + 2)x + 4 is always positive

• here coefficient of x² is positive and expression should be positive then

$∆ < 0$

so, for expression ax² + bx + c

$b ^{2} - 4ac < 0$

• here a = 1; b = -(a + 2); c = 4

• so, {-(a + 2)}² - (4)(1)(4) < 0

• a² + 4a + 4 - 16 < 0

• a² + 4a - 12 < 0

• a² + 6a - 2a - 12 < 0

• a(a + 6) -2(a + 6) < 0

• (a + 6)(a - 2) < 0

• so, -6 < a < 2

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• question number 7 is not clear. Please give the equation clearly